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Geodesy for Gravity and Height Systems

A special issue of Remote Sensing (ISSN 2072-4292). This special issue belongs to the section "Remote Sensing in Geology, Geomorphology and Hydrology".

Deadline for manuscript submissions: closed (31 October 2021) | Viewed by 66346

Special Issue Editors

Prof. Dr. Roland Pail

E-Mail Website
Guest Editor
Technical University of Munich, Institute of Astronomical and Physical Geodesy, Arcisstrasse 21, 80333 Munich, Germany
Interests: physical geodesy; satellite geodesy
Prof. Dr. Pavel Novák

E-Mail Website
Guest Editor
Department of Geomatics, University of West Bohemia, Univerzitní 22, Plze, CZ-306 14 Pilsen, Czech Republic
Interests: gravity; mathematical and theoretical geodesy
Dr. George Vergos

E-Mail Website
Guest Editor
Laboratory of Gravity Field Research and Applications—GravLab, Aristotle University of Thessaloniki, Thessaloniki, Greece
Interests: gravity and geoid modeling; satellite altimetry; height systems
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Geodesy in general and gravity field modeling in particular have become important disciplines of remote sensing of our planet and provide unique products that are used by many geoscientific disciplines. From the classical disciplines of geoid determination, geodetic reference systems realization, navigation and satellite orbit determination, and geophysics and interior earth structure, the gravity field science has in recent decades provided unique data on mass transport processes in the Earth system, such as changes in the water cycle and ice mass melting, primarily due to the GRACE and GRACE-Follow On satellite missions. At the same time, global knowledge of the gravity field details has improved significantly due to the GOCE mission, large-scale airborne gravity campaigns, and the coverage of the oceans by satellite altimetry. New technologies such as cold atom interferometry, miniature gravity sensors, strap-down IMU gravity sensors, and new satellite mission concepts are going to further advance gravity field science.

This Special Issue solicits contributions that focus on all aspects of global and regional gravity field determination, from theoretical and methodological issues to modeling results and applications. We seek contributions that focus on absolute and relative gravimetry, instrumentation and new sensors, gravity field theory, global and regional gravity field modeling at all spatial and temporal scales, and geophysical and oceanographic applications of gravity field models. Theory, methodology, and practical aspects of height system unification will also be a focus element, as well as current and future gravity field missions for monitoring mass transport processes in the Earth system.

Prof. Dr. Roland Pail
Prof. Dr. Pavel Novák
Prof. Dr. George Vergos
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Remote Sensing is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2700 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Gravity field modeling
  • Geoid
  • Height systems
  • Gravimetry
  • Satellite gravity missions
  • Satellite altimetry
  • Mass transport

Published Papers (21 papers)

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22 pages, 4765 KiB  
Article
Data Processing of Gravity Base Network in Plateau Area: The Case of Qinghai Province, China
by Qiong Wu, Shi Liu, Bin Wang, Linshan Zhong, Lijiang Zhao, Shengpeng Zhang and Hongqing Li
Remote Sens. 2022, 14(5), 1142; https://0-doi-org.brum.beds.ac.uk/10.3390/rs14051142 - 25 Feb 2022
Viewed by 1570
Abstract
The latest gravity survey of the gravity base network in Qinghai Province, China, was conducted with six Scintrex CG gravimeters and this gravity survey was tied to existed gravity reference stations. In this gravity network with long segments and very rugged topography, the [...] Read more.
The latest gravity survey of the gravity base network in Qinghai Province, China, was conducted with six Scintrex CG gravimeters and this gravity survey was tied to existed gravity reference stations. In this gravity network with long segments and very rugged topography, the calibration of scale factors is a time-consuming progress and its accuracy may be affected by many uncertainties, and the change in drift rates of the relative gravimeters are complex over time in this long-term survey. The reasonable calculation of scale factors and drift rates plays an important role in improving the gravity estimation accuracy. In this paper, based on the least squares, robust least squares, and Bayesian methods, various parameter calculation methods were employed to process this gravity network. The performance and practicality of each method were analyzed in terms of internal and external accuracy. The results indicated that the scale factors calibrated in the baseline field had poor applicability due to insufficient gravity difference, in this case, the scale factors estimated by the adjustment models were more accurate, which weakened the correlation between gravity differences and mutual differences. The drift rates estimated by the Bayesian method were relatively smooth over time, while drift rates estimated using symmetric observations were more practical for the gravimeter with highly variable drift. The weight constraints of observations can be optimized by the robust least squares method, the gravity values obtained by it were more consistent with absolute gravity values than those obtained by the least squares method, and the robust least squares method was recommended to process gravity data in plateau areas. Full article
(This article belongs to the Special Issue Geodesy for Gravity and Height Systems)
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24 pages, 13059 KiB  
Article
Treatment of Tide Gauge Time Series and Marine GNSS Measurements for Vertical Land Motion with Relevance to the Implementation of the Baltic Sea Chart Datum 2000
by Sander Varbla, Jonas Ågren, Artu Ellmann and Markku Poutanen
Remote Sens. 2022, 14(4), 920; https://0-doi-org.brum.beds.ac.uk/10.3390/rs14040920 - 14 Feb 2022
Cited by 13 | Viewed by 2317
Abstract
Tide gauge (TG) time series and GNSS measurements have become standard datasets for various scientific and practical applications. However, the TG and geodetic networks in the Baltic Sea region are deforming due to vertical land motion (VLM), the primary cause of which is [...] Read more.
Tide gauge (TG) time series and GNSS measurements have become standard datasets for various scientific and practical applications. However, the TG and geodetic networks in the Baltic Sea region are deforming due to vertical land motion (VLM), the primary cause of which is the glacial isostatic adjustment. Consequently, a correction for VLM, either obtained from a suitable VLM model or by utilizing space-geodetic techniques, must be applied to ensure compatibility of various data sources. It is common to consider the VLM rate relative to an arbitrary reference epoch, but this also yields that the resulting datasets may not be directly comparable. The common height reference, Baltic Sea Chart Datum 2000 (BSCD2000), has been initiated to facilitate the effective use of GNSS methods for accurate navigation and offshore surveying. The BSCD2000 agrees with the current national height realizations of the Baltic Sea countries. As TGs managed by national authorities are rigorously connected to the national height systems, the TG data can also be used in a common system. Hence, this contribution aims to review the treatment of TG time series for VLM and outline potential error sources for utilizing TG data relative to a common reference. Similar consideration is given for marine GNSS measurements that likewise require VLM correction for some marine applications (such as validating marine geoid models). The described principles are illustrated by analyzing and discussing numerical examples. These include investigations of TG time series and validation of shipborne GNSS determined sea surface heights. The latter employs a high-resolution geoid model and hydrodynamic model-based dynamic topography, which is linked to the height reference using VLM corrected TG data. Validation of the presented VLM corrected marine GNSS measurements yields a 1.7 cm standard deviation and −2.7 cm mean residual. The estimates are 1.9 cm and −10.2 cm, respectively, by neglecting VLM correction. The inclusion of VLM correction thus demonstrates significant improvement toward data consistency. Although the focus is on the Baltic Sea region, the principles described here are also applicable elsewhere. Full article
(This article belongs to the Special Issue Geodesy for Gravity and Height Systems)
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25 pages, 4696 KiB  
Article
Insights into Seismogenetic Areas in Central Italy from Combined Absolute Gravity and GNSS Measurements
by Filippo Greco, Federica Riguzzi and Giovanna Berrino
Remote Sens. 2021, 13(22), 4649; https://0-doi-org.brum.beds.ac.uk/10.3390/rs13224649 - 18 Nov 2021
Cited by 2 | Viewed by 2351
Abstract
In this study we present and discuss gravity and ground deformation variations, at different time scales, observed in a wide mesh absolute gravity and GNSS network set up in central Italy. The network was installed in the area affected by the 2009 (L’Aquila; [...] Read more.
In this study we present and discuss gravity and ground deformation variations, at different time scales, observed in a wide mesh absolute gravity and GNSS network set up in central Italy. The network was installed in the area affected by the 2009 (L’Aquila; Mw 6.1) and 2016 (Amatrice-Norcia; Mw 6.0 and 6.5) seismic activity, in order to verify if gravity and ground deformation variations could be related to seismic effects. The new network includes 5 stations distributed between the Lazio, Umbria, and Abruzzo regions. From 2018 to 2020 three campaigns were carried out using the transportable Micro-g LaCoste FG5#238 and the portable Micro-g LaCoste A10#39 absolute gravimeters and completed with two simultaneous GNSS measurements. Topographic instruments, measurement and analysis techniques enabling accurate measurements in the positioning of the stations and to control their variations over time were applied. The high reliability and accuracy of the absolute gravity data gathered, after being corrected for known effects, showed a negative short-term (2018–2020) pattern throughout the area, up to −30 µGal. Since some stations of the new network coincided with benchmarks already measured in the past, an analysis of long-term gravity changes was carried out and a fair degree of stability was observed in two stations, while positive large variations, of approximately 70 and 157 µGal, were recorded in the other two stations in the time intervals 1954–2020 and 2005–2010, respectively. On the other hand, variations highlighted by GNSS height measurements were all below 3 cm. Here, the first long-lasting gravity measurements carried out with absolute gravimeters in a seismic area in Italy are presented, providing meaningful geophysical information. The obtained results, in terms of availability of a combined absolute gravity and GNSS network, definition of data acquisition and analysis procedures, as well as creation of a high quality data archive, lay the foundations for a multidisciplinary approach towards improving the knowledge of this seismogenetic area of Italy. Full article
(This article belongs to the Special Issue Geodesy for Gravity and Height Systems)
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32 pages, 5286 KiB  
Article
Next Generation Gravity Mission Elements of the Mass Change and Geoscience International Constellation: From Orbit Selection to Instrument and Mission Design
by Luca Massotti, Christian Siemes, Günther March, Roger Haagmans and Pierluigi Silvestrin
Remote Sens. 2021, 13(19), 3935; https://0-doi-org.brum.beds.ac.uk/10.3390/rs13193935 - 01 Oct 2021
Cited by 24 | Viewed by 3180
Abstract
ESA’s Next Generation Gravity Mission (NGGM) is a candidate Mission of Opportunity for ESA–NASA cooperation in the frame of the Mass Change and Geosciences International Constellation (MAGIC). The mission aims at enabling long-term monitoring of the temporal variations of Earth’s gravity field at [...] Read more.
ESA’s Next Generation Gravity Mission (NGGM) is a candidate Mission of Opportunity for ESA–NASA cooperation in the frame of the Mass Change and Geosciences International Constellation (MAGIC). The mission aims at enabling long-term monitoring of the temporal variations of Earth’s gravity field at relatively high temporal (down to 3 days) and increased spatial resolutions (up to 100 km) at longer time intervals. This implies also that time series of GRACE and GRACE-FO can be extended towards a climate series. Such variations carry information about mass change induced by the water cycle and the related mass exchange among atmosphere, oceans, cryosphere, land and solid Earth and will complete our picture of global and climate change. The main observable is the variation of the distance between two satellites measured by a ranging instrument. This is complemented by accelerometers that measure the nongravitational accelerations, which need to be reduced from ranging measurements to obtain the gravity signal. The preferred satellite constellation comprises one satellite pair in a near-polar and another in an inclined circular orbit. The paper focuses on the orbit selection methods for optimizing the spatial sampling for multiple temporal resolutions and then on the methodology for deriving the engineering requirements for the space segment, together with a discussion on the main mission parameters. Full article
(This article belongs to the Special Issue Geodesy for Gravity and Height Systems)
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18 pages, 7355 KiB  
Article
Lithospheric Equilibrium, Environmental Changes, and Potential Induced-Earthquake Risk around the Newly Impounded Baihetan Reservoir, China
by Guangyu Fu, Yawen She, Guoqing Zhang, Yun Wang, Shanghua Gao and Tai Liu
Remote Sens. 2021, 13(19), 3895; https://0-doi-org.brum.beds.ac.uk/10.3390/rs13193895 - 29 Sep 2021
Cited by 6 | Viewed by 1799
Abstract
The Baihetan hydropower station is the second largest hydropower station worldwide. It began to store water in April 2021. We conducted a dense hybrid gravity and GNSS survey at 223 stations, obtained the free-air and Bouguer gravity anomalies, inversed the lithospheric density structure, [...] Read more.
The Baihetan hydropower station is the second largest hydropower station worldwide. It began to store water in April 2021. We conducted a dense hybrid gravity and GNSS survey at 223 stations, obtained the free-air and Bouguer gravity anomalies, inversed the lithospheric density structure, and calculated the isostatic additional force (IAF) borne by lithosphere in the reservoir area. Moreover, we studied the gravity change and Coulomb stress change around the Baihetan reservoir due to impoundment. The main findings are the following. (1) Hybrid gravity and GNSS observations significantly improved the spatial resolution of the gravity field, and the maximum improvement reached up to 150 mGal. (2) A new method for risk assessment of reservoir-induced earthquakes is proposed from the perspective of lithospheric equilibrium. It was found that there is an IAF of −30 MPa at approximately 20 km upstream of the Baihetan dam, and the risk of a reservoir-induced earthquake in this area warrants attention. (3) It was found that the Coulomb stress variation on the Xiaojiang fault near Qiaojia at a depth of 10 km exceeded the threshold for inducing an earthquake (0.1 bar). Full article
(This article belongs to the Special Issue Geodesy for Gravity and Height Systems)
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22 pages, 7342 KiB  
Article
Validation of GRACE and GRACE-FO Mascon Data for the Study of Polar Motion Excitation
by Justyna Śliwińska, Małgorzata Wińska and Jolanta Nastula
Remote Sens. 2021, 13(6), 1152; https://0-doi-org.brum.beds.ac.uk/10.3390/rs13061152 - 17 Mar 2021
Cited by 10 | Viewed by 2469
Abstract
In this study, we calculate the hydrological plus cryospheric excitation of polar motion (hydrological plus cryospheric angular momentum, HAM/CAM) using mascon solutions based on observations from the Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On (GRACE-FO) missions. We compare and evaluate HAM/CAM [...] Read more.
In this study, we calculate the hydrological plus cryospheric excitation of polar motion (hydrological plus cryospheric angular momentum, HAM/CAM) using mascon solutions based on observations from the Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On (GRACE-FO) missions. We compare and evaluate HAM/CAM computed from GRACE and GRACE-FO mascon data provided by the Jet Propulsion Laboratory (JPL), the Center for Space Research (CSR), and the Goddard Space Flight Center (GSFC). A comparison with HAM obtained from the Land Surface Discharge Model is also provided. An analysis of HAM/CAM and HAM is performed for overall variability, trends, and seasonal and non-seasonal variations. The HAM/CAM and HAM estimates are validated using the geodetic residual time series (GAO), which is an estimation of the hydrological plus cryospheric signal in geodetically observed polar motion excitation. In general, all mascon datasets are found to be equally suitable for the determination of overall, seasonal, and non-seasonal HAM/CAM oscillations, but some differences in trends remain. The use of an ellipsoidal correction, implemented in the newest solution from CSR, does not noticeably affect the consistency between HAM/CAM and GAO. Analysis of the data from the first two years of the GRACE-FO mission indicates that the current accuracy of HAM/CAM from GRACE-FO mascon data meets expectations, and the root mean square deviation of HAM/CAM components are between 5 and 6 milliarcseconds. The findings from this study can be helpful in assessing the role of satellite gravimetry in polar motion studies and may contribute towards future improvements to GRACE-FO data processing. Full article
(This article belongs to the Special Issue Geodesy for Gravity and Height Systems)
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23 pages, 4314 KiB  
Article
Geodetic-Gravimetric Monitoring of Mountain Uplift and Hydrological Variations at Zugspitze and Wank Mountains (Bavarian Alps, Germany)
by Ludger Timmen, Christian Gerlach, Till Rehm, Christof Völksen and Christian Voigt
Remote Sens. 2021, 13(5), 918; https://0-doi-org.brum.beds.ac.uk/10.3390/rs13050918 - 01 Mar 2021
Cited by 6 | Viewed by 3097
Abstract
In 2004, first absolute gravity (AG) measurements were performed on the top of Mt. Zugspitze (2 sites) and at the foot (1 site) and top (1 site) of Mt. Wank. Mt. Wank (summit height 1780 m) and Mt. Zugspitze (2960 m) are about [...] Read more.
In 2004, first absolute gravity (AG) measurements were performed on the top of Mt. Zugspitze (2 sites) and at the foot (1 site) and top (1 site) of Mt. Wank. Mt. Wank (summit height 1780 m) and Mt. Zugspitze (2960 m) are about 15 km apart from each other and belong geologically to different parts of the Northern Limestone Alps. Bridging a time span of 15 years, the deduced gravity variations for Zugspitze are in the order of −0.30 μm/s2 with a standard uncertainty of 0.04 μm/s2. The Wank stations (foot and top) show no significant gravity variation. The vertical stability of Wank summit is also confirmed by results of continuous GNSS recordings. Because an Alpine mountain uplift of 1 or 2 mm/yr cannot explain the obtained gravity decline at Zugspitze, the dominating geophysical contributions are assumed to be due to the diminishing glaciers in the vicinity. The modelled gravity trend caused by glacier retreat between epochs 1999 and 2018 amounts to −0.012 μm/s2/yr at both Zugspitze AG sites. This explains more than half of the observed gravity decrease. Long-term variations on inter-annual and climate-relevant decadal scale will be investigated in the future using as supplement superconducting gravimetry (installed in 2019) and GNSS equipment (since 2018). Full article
(This article belongs to the Special Issue Geodesy for Gravity and Height Systems)
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17 pages, 3491 KiB  
Article
Refining Altimeter-Derived Gravity Anomaly Model from Shipborne Gravity by Multi-Layer Perceptron Neural Network: A Case in the South China Sea
by Chengcheng Zhu, Jinyun Guo, Jiajia Yuan, Xin Jin, Jinyao Gao and Chengming Li
Remote Sens. 2021, 13(4), 607; https://0-doi-org.brum.beds.ac.uk/10.3390/rs13040607 - 08 Feb 2021
Cited by 8 | Viewed by 2043
Abstract
Shipborne gravity can be used to refine altimeter-derived gravity whose accuracy is low in shallow waters and areas with complex submarine topography. As altimeter-derived gravity only within a small radius around the shipborne data can be corrected by traditional methods, a new method [...] Read more.
Shipborne gravity can be used to refine altimeter-derived gravity whose accuracy is low in shallow waters and areas with complex submarine topography. As altimeter-derived gravity only within a small radius around the shipborne data can be corrected by traditional methods, a new method based on multi-layer perceptron (MLP) neural network is proposed to refine the altimeter-derived gravity. Input variables of MLP include the positional information at observation points and geophysical information (from our own South China Sea gravity anomaly model (SCSGA) V1.0 and bathymetry model ETOPO1) at grid points around observation points. Output variables of MLP are the refined residual gravity anomalies at observation points. Training shipborne data are classified into four cases to train four MLP models, which are used to predict the refined gravity anomaly model SCSGA V1.1. Then all of the training shipborne data are used for training an MLP model to predict the refined gravity anomaly model SCSGA V1.2. Assessed by testing shipborne data, the accuracy of SCSGA V1.2 is 0.14 mGal higher than that of SCSGA V1.0, and similar to that of SCSGA V1.1. Compared with the original gravity anomaly model (SCSGA V1.0), the accuracy of the refined gravity anomaly model (SCSGA V1.2) by MLP is improved by 4.4% in areas where the training data are concentrated, and also improved by 2.2% in other areas. Therefore, the method of MLP can be used to refine the altimeter-derived gravity model by shipborne gravity, overcoming the problem of limited correction radius for traditional methods. Full article
(This article belongs to the Special Issue Geodesy for Gravity and Height Systems)
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23 pages, 10275 KiB  
Article
Estimation of Vertical Datum Parameters Using the GBVP Approach Based on the Combined Global Geopotential Models
by Panpan Zhang, Lifeng Bao, Dongmei Guo, Lin Wu, Qianqian Li, Hui Liu, Zhixin Xue and Zhicai Li
Remote Sens. 2020, 12(24), 4137; https://0-doi-org.brum.beds.ac.uk/10.3390/rs12244137 - 17 Dec 2020
Cited by 9 | Viewed by 2271
Abstract
Unification of the global vertical datum has been a key problem to be solved for geodesy over a long period, and the main challenge for a unified vertical datum system is to determine the vertical offset between the local vertical datum and the [...] Read more.
Unification of the global vertical datum has been a key problem to be solved for geodesy over a long period, and the main challenge for a unified vertical datum system is to determine the vertical offset between the local vertical datum and the global vertical datum. For this purpose, the geodetic boundary value problem (GBVP) approach based on the remove-compute-restore (RCR) technique is used to determine the vertical datum parameters in this paper. In the RCR technique, a global geopotential model (GGM) is required to remove and restore the long wavelengths of the gravity field. The satellite missions of the GRACE (Gravity Recovery and Climate Experiment) and GOCE (Gravity field and steady-state Ocean Circulation Exploration) offer high accuracy medium–long gravity filed information, but GRACE/GOCE-based GGMs are restricted to medium–long wavelengths because the maximum degree of their spherical harmonic representation is limited, which is known as an omission error. To compensate for the omission error of GRACE/GOCE-based GGM, a weighting method is used to determine the combined GGM by combining the high-resolution EGM2008 model (Earth Gravitational Model 2008) and GRACE/GOCE-based GGM to effectively bridge the spectral gap between satellite and terrestrial data. An additional consideration for the high-frequency gravity signals is induced by the topography, and the residual terrain model (RTM) is used to recover the omission errors effect of the combined GGM. In addition, to facilitate practical implementation of the GBVP approach, the effects of the indirect bias term, the spectral accuracy of the GGM, and the systematic levelling errors and distortions in estimations of the vertical datum parameters are investigated in this study. Finally, as a result of the GBVP solution based on the combined DIR_R6/EGM2008 model, RTM, and residual gravity, the geopotential values of the North American Vertical Datum of 1988 (NAVD88), the Australian Height Datum (AHD), and the Hong Kong Principal Datum (HKPD) are estimated to be equal to 62636861.31 ± 0.96, 62653852.60 ± 0.95 and 62636860.55 ± 0.29 m2s−2, respectively. The vertical offsets of NAVD88, AHD, and HKPD with respect to the global geoid are estimated as −0.809 ± 0.090, 0.082 ± 0.093, and −0.731 ± 0.030 m, respectively. Full article
(This article belongs to the Special Issue Geodesy for Gravity and Height Systems)
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14 pages, 2943 KiB  
Article
On the Feasibility of Seafloor Topography Estimation from Airborne Gravity Gradients: Performance Analysis Using Real Data
by Junjun Yang, Zhicai Luo, Liangcheng Tu, Shanshan Li, Jingxue Guo and Diao Fan
Remote Sens. 2020, 12(24), 4092; https://0-doi-org.brum.beds.ac.uk/10.3390/rs12244092 - 15 Dec 2020
Cited by 5 | Viewed by 2186
Abstract
Compared with airborne gravimetry, a technique frequently used to infer the seafloor topography at places inaccessible to ship soundings due to the presence of ice shelf or ice mélange, airborne gravity gradiometry inherently could achieve higher spatial resolution, thus it is promising for [...] Read more.
Compared with airborne gravimetry, a technique frequently used to infer the seafloor topography at places inaccessible to ship soundings due to the presence of ice shelf or ice mélange, airborne gravity gradiometry inherently could achieve higher spatial resolution, thus it is promising for improved inference of seafloor topography. However, its estimation capability has not been demonstrated by real projects. Theoretical analysis through admittance shows that compared with gravity disturbance, gravity gradient is more sensitive to the short-wavelength seafloor topography but diminishes faster with the increase of the distance between the seafloor and airplane, indicating its superiority is recovering short-wavelength topographic features over shallow waters. We present the first numerical experiment that estimates seafloor topography from a 0.4-km resolution, real airborne gravity gradients. It is shown that airborne gravity gradiometry can recover smaller topographic features than typical airborne gravimetry, but the estimation accuracy is only ±17 m due to the presence of subsurface density variations. The long-wavelength effect of the subsurface density variations can be removed with the aid of constraining bathymetry inside the study area, whereas the short wavelengths cannot. This study expands the applications of airborne gravity gradiometry, and helps glaciologists understand its performance in seafloor topography estimation. Full article
(This article belongs to the Special Issue Geodesy for Gravity and Height Systems)
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30 pages, 4624 KiB  
Article
Geodetic SAR for Height System Unification and Sea Level Research—Observation Concept and Preliminary Results in the Baltic Sea
by Thomas Gruber, Jonas Ågren, Detlef Angermann, Artu Ellmann, Andreas Engfeldt, Christoph Gisinger, Leszek Jaworski, Simo Marila, Jolanta Nastula, Faramarz Nilfouroushan, Xanthi Oikonomidou, Markku Poutanen, Timo Saari, Marius Schlaak, Anna Światek, Sander Varbla and Ryszard Zdunek
Remote Sens. 2020, 12(22), 3747; https://0-doi-org.brum.beds.ac.uk/10.3390/rs12223747 - 14 Nov 2020
Cited by 8 | Viewed by 4514
Abstract
Traditionally, sea level is observed at tide gauge stations, which usually also serve as height reference stations for national leveling networks and therefore define a height system of a country. One of the main deficiencies to use tide gauge data for geodetic sea [...] Read more.
Traditionally, sea level is observed at tide gauge stations, which usually also serve as height reference stations for national leveling networks and therefore define a height system of a country. One of the main deficiencies to use tide gauge data for geodetic sea level research and height systems unification is that only a few stations are connected to the geometric network of a country by operating permanent GNSS receivers next to the tide gauge. As a new observation technique, absolute positioning by SAR using active transponders on ground can fill this gap by systematically observing time series of geometric heights at tide gauge stations. By additionally knowing the tide gauge geoid heights in a global height reference frame, one can finally obtain absolute sea level heights at each tide gauge. With this information the impact of climate change on the sea level can be quantified in an absolute manner and height systems can be connected across the oceans. First results from applying this technique at selected tide gauges at the Baltic coasts are promising but also exhibit some problems related to the new technique. The paper presents the concept of using the new observation type in an integrated sea level observing system and provides some early results for SAR positioning in the Baltic sea area. Full article
(This article belongs to the Special Issue Geodesy for Gravity and Height Systems)
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35 pages, 17962 KiB  
Article
Temporal Gravity Signals in Reprocessed GOCE Gravitational Gradients
by Betty Heller, Frank Siegismund, Roland Pail, Thomas Gruber and Roger Haagmans
Remote Sens. 2020, 12(21), 3483; https://0-doi-org.brum.beds.ac.uk/10.3390/rs12213483 - 23 Oct 2020
Cited by 3 | Viewed by 2449
Abstract
The reprocessing of the satellite gravitational gradiometry (SGG) data from the Gravity field and steady-state Ocean Circulation Explorer (GOCE) satellite mission in 2018/2019 considerably reduced the low-frequency noise in the data, leading to reduced noise amplitudes in derived gravity field models at large [...] Read more.
The reprocessing of the satellite gravitational gradiometry (SGG) data from the Gravity field and steady-state Ocean Circulation Explorer (GOCE) satellite mission in 2018/2019 considerably reduced the low-frequency noise in the data, leading to reduced noise amplitudes in derived gravity field models at large spatial scales, at which temporal variations of the Earth’s gravity field have their highest amplitudes. This is the motivation to test the reprocessed GOCE SGG data for their ability to resolve time-variable gravity signals. For the gravity field processing, we apply and compare a spherical harmonics (SH) approach and a mass concentration (mascon) approach. Although their global signal-to-noise ratio is <1, SH GOCE SGG-only models resolve the strong regional signals of glacier melting in Greenland and Antarctica, and the 2011 moment magnitude 9.0 earthquake in Japan, providing an estimation of gravity variations independent of Gravity Recovery and Climate Experiment (GRACE) data. The benefit of combined GRACE/GOCE SGG models is evaluated based on the ice mass trend signals in Greenland and Antarctica. While no signal contribution from GOCE SGG data additional to the GRACE models could be observed, we show that the incorporation of GOCE SGG data numerically stabilizes the related normal equation systems. Full article
(This article belongs to the Special Issue Geodesy for Gravity and Height Systems)
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20 pages, 8496 KiB  
Article
Assessment of Temporal Variations of Orthometric/Normal Heights Induced by Hydrological Mass Variations over Large River Basins Using GRACE Mission Data
by Walyeldeen Godah, Malgorzata Szelachowska, Jan Krynski and Jagat Dwipendra Ray
Remote Sens. 2020, 12(18), 3070; https://0-doi-org.brum.beds.ac.uk/10.3390/rs12183070 - 19 Sep 2020
Cited by 5 | Viewed by 2946
Abstract
Almost half of the Earth’s land is covered by large river basins. Temporal variations of hydrological masses induce time-varying gravitational potential and temporal mass loading that deforms the Earth’s surface. These phenomena cause temporal variations of geoid/quasigeoid and ellipsoidal heights that result in [...] Read more.
Almost half of the Earth’s land is covered by large river basins. Temporal variations of hydrological masses induce time-varying gravitational potential and temporal mass loading that deforms the Earth’s surface. These phenomena cause temporal variations of geoid/quasigeoid and ellipsoidal heights that result in temporal variations of orthometric/normal heights ΔH/ΔH*. The aim of this research is to assess ΔH/ΔH* induced by hydrological masses over large river basins using the Gravity Recovery and Climate Experiment (GRACE) satellite mission data. The results obtained reveal that for the river basin of a strong hydrological signal, ΔH/ΔH* reach 8 cm. These ΔH/ΔH* would be needed to reliably determine accurate orthometric/normal heights. The ΔH/ΔH* do not exceed ±1 cm in the case of the river basin of the weak hydrological signal. The relation between hydrological mass changes and ΔH/ΔH* was investigated. Correlations between ΔH/ΔH* and temporal variations of equivalent water thickness were observed in 87% of river basins subareas out of which 45% exhibit strong correlations. The ΔH/ΔH* determined over two river basins that characterize with the strongest and weakest temporal variations were analysed using the Principal Component Analysis method. The results obtained reveal that ΔH/ΔH* in subareas of the same river basin can significantly differ (e.g., ±2 cm in the Amazon basin) from each other, and are strongly associated with different spatio-temporal patterns of the entire river basin. Full article
(This article belongs to the Special Issue Geodesy for Gravity and Height Systems)
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28 pages, 6599 KiB  
Article
Improved Estimation of Regional Surface Mass Variations from GRACE Intersatellite Geopotential Differences Using a Priori Constraints
by Bo Zhong, Qiong Li, Jianli Chen, Zhicai Luo and Hao Zhou
Remote Sens. 2020, 12(16), 2553; https://0-doi-org.brum.beds.ac.uk/10.3390/rs12162553 - 08 Aug 2020
Cited by 14 | Viewed by 2925
Abstract
We presented an improved method for estimation of regional surface mass variations from the Gravity Recovery and Climate Experiment (GRACE)-derived precise intersatellite geopotential differences using a priori constraints. An alternative analytic formula was proposed to incorporate the K-band ranging (KBR) range rate into [...] Read more.
We presented an improved method for estimation of regional surface mass variations from the Gravity Recovery and Climate Experiment (GRACE)-derived precise intersatellite geopotential differences using a priori constraints. An alternative analytic formula was proposed to incorporate the K-band ranging (KBR) range rate into the improved energy balance equation, and precise geopotential differences were estimated from GRACE Level-1B data based on the remove-compute-restore (RCR) technique, which avoids the long-wavelength gravity signals being absorbed by empirical parameters. To reduce the ill condition for inversion of regional mass variations from geopotential differences, a priori information from hydrological models was used to construct the constraint equations, and the optimal regularization parameters were adaptively determined based on iterative least-squares estimation. To assess our improved method, a case study of regional mass variations’ inversion was carried out over South America on 2° × 2° grids at monthly intervals from January 2005 to December 2010. The results show that regional mascon solutions inverted from geopotential differences estimated by the RCR technique using hydrological models as a priori constraints can retain more signal energy and enhance regional mass variation inversion. The spatial distributions and annual amplitudes of geopotential difference-based regional mascon solutions agree well with the official GRACE mascon solutions, although notable differences exist in spatial patterns and trends, especially in small basins. In addition, our improved method can robustly estimate the mascon solutions, which are less affected by the a priori information. The results from the case study have clearly demonstrated the feasibility and effectiveness of the proposed method. Full article
(This article belongs to the Special Issue Geodesy for Gravity and Height Systems)
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18 pages, 4987 KiB  
Article
Centimeter Precision Geoid Model for Jeddah Region (Saudi Arabia)
by Alessandra Borghi, Riccardo Barzaghi, Omar Al-Bayari and Suhail Al Madani
Remote Sens. 2020, 12(12), 2066; https://0-doi-org.brum.beds.ac.uk/10.3390/rs12122066 - 26 Jun 2020
Cited by 8 | Viewed by 3151
Abstract
In 2014, the Jeddah Municipality made a call for an estimate of a centimetric precision geoid model to be used for engineering and surveying applications, because the regional geoid model available at that time did not reach a sufficient precision. A project was [...] Read more.
In 2014, the Jeddah Municipality made a call for an estimate of a centimetric precision geoid model to be used for engineering and surveying applications, because the regional geoid model available at that time did not reach a sufficient precision. A project was set up to this end and dedicated sets of gravity and Global Positioning System (GPS)/levelling data were acquired in the framework of this project. In this paper, a thorough analysis of these newly acquired data and of the last available Global Gravity Field Models (GGMs) has been done in order to obtain a geoid undulation estimate with the prescribed precision. In the framework of the Remove–Compute–Restore (RCR) approach, the collocation method was used to obtain the height anomaly estimation that was then converted to geoid undulation. The remove and restore steps of the RCR approach were based on GGMs, derived from the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) and Gravity Recovery and Climate Experiment (GRACE) dedicated gravity satellite missions, which were used to improve the long wavelength components of the Earth’s gravity field. Furthermore, two different quasi-geoid collocation estimates were computed, based on gravity data only and on gravity plus GPS/levelling data (the so-called hybrid estimate). The best solutions were obtained with the hybrid geoid estimate. This was tested by comparison with an independent set of GPS/levelling geoid undulations that were not included in the computed solutions. By these tests, the precision of the hybrid geoid is estimated to be 3.7 cm. This precision proved to be better, by a factor of two, than the corresponding one estimated from the pure gravimetric geoid. This project has been also useful to verify the importance and reliability of GGMs developed from the last satellite gravity missions (GOCE and GRACE) that have significantly improved our knowledge of the long wavelength components of the Earth’s gravity field, especially in areas with poor coverage of terrestrial gravity data. In fact, the geoid models based on satellite-only GGMs proved to have a better performance, despite the lower spatial resolution with respect to high-resolution models (i.e., Earth Gravitational Model 2008 (EGM2008)). Full article
(This article belongs to the Special Issue Geodesy for Gravity and Height Systems)
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25 pages, 3209 KiB  
Article
Determination of the Regularization Parameter to Combine Heterogeneous Observations in Regional Gravity Field Modeling
by Qing Liu, Michael Schmidt, Roland Pail and Martin Willberg
Remote Sens. 2020, 12(10), 1617; https://0-doi-org.brum.beds.ac.uk/10.3390/rs12101617 - 19 May 2020
Cited by 5 | Viewed by 3251
Abstract
Various types of heterogeneous observations can be combined within a parameter estimation process using spherical radial basis functions (SRBFs) for regional gravity field refinement. In this process, regularization is in most cases inevitable, and choosing an appropriate value for the regularization parameter is [...] Read more.
Various types of heterogeneous observations can be combined within a parameter estimation process using spherical radial basis functions (SRBFs) for regional gravity field refinement. In this process, regularization is in most cases inevitable, and choosing an appropriate value for the regularization parameter is a crucial issue. This study discusses the drawbacks of two frequently used methods for choosing the regularization parameter, which are the L-curve method and the variance component estimation (VCE). To overcome their drawbacks, two approaches for the regularization parameter determination are proposed, which combine the L-curve method and VCE. The first approach, denoted as “VCE-Lc”, starts with the calculation of the relative weights between the observation techniques by means of VCE. Based on these weights, the L-curve method is applied to determine the regularization parameter. In the second approach, called “Lc-VCE”, the L-curve method determines first the regularization parameter, and it is set to be fixed during the calculation of the relative weights between the observation techniques from VCE. To evaluate and compare the performance of the two proposed methods with the L-curve method and VCE, all these four methods are applied in six study cases using four types of simulated observations in Europe, and their modeling results are compared with the validation data. The RMS errors (w.r.t the validation data) obtained by VCE-Lc and Lc-VCE are smaller than those obtained from the L-curve method and VCE in all the six cases. VCE-Lc performs the best among these four tested methods, no matter if using SRBFs with smoothing or non-smoothing features. These results prove the benefits of the two proposed methods for regularization parameter determination when different data sets are to be combined. Full article
(This article belongs to the Special Issue Geodesy for Gravity and Height Systems)
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21 pages, 7930 KiB  
Article
TGF: A New MATLAB-based Software for Terrain-related Gravity Field Calculations
by Meng Yang, Christian Hirt and Roland Pail
Remote Sens. 2020, 12(7), 1063; https://0-doi-org.brum.beds.ac.uk/10.3390/rs12071063 - 26 Mar 2020
Cited by 18 | Viewed by 7011
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Geodesy for Gravity and Height Systems)
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22 pages, 5872 KiB  
Article
Triple-Pair Constellation Configurations for Temporal Gravity Field Retrieval
by Anna F. Purkhauser and Roland Pail
Remote Sens. 2020, 12(5), 831; https://0-doi-org.brum.beds.ac.uk/10.3390/rs12050831 - 04 Mar 2020
Cited by 5 | Viewed by 3878
Abstract
The goal of next-generation gravity missions (NGGM) is to improve the monitoring of mass transport in the Earth system by an increased space-time sampling capability as well as higher accuracies of a new generation of instrumentation, but also to continue the monitoring time [...] Read more.
The goal of next-generation gravity missions (NGGM) is to improve the monitoring of mass transport in the Earth system by an increased space-time sampling capability as well as higher accuracies of a new generation of instrumentation, but also to continue the monitoring time series obtained by past and current missions such as GRACE and GRACE Follow-On. As the likelihood of three satellite pairs being simultaneously in orbit in the mid-term future increased, we have performed a closed-loop simulation to investigate the impact of a third pair in either polar or inclined orbit as an addition to a Bender-type constellation with NGGM instrumentation. For the additional pair, GRACE-like as well as NGGM instrumentation was tested. The analysis showed that the third pair mainly increases the redundancy of the monitoring system but does not significantly improve de-aliasing capabilities. The best-performing triple-pair scenario comprises a third inclined pair with NGGM sensors. Starting with a Bender-type constellation of a polar and an inclined satellite pair, simulation results indicate an average improvement of 11% in case of adding the third pair in a near-polar orbit, and of 21% for the third pair placed in an inclined orbit. The most important advantage of a multi-pair constellation, however, is the possibility to recover daily gravity fields with higher spatial resolution. In the case of the investigated triple-pair scenarios, a meaningful daily resolution with a maximum spherical harmonic degree of 26 can be achieved, while a higher daily parametrization up to degree 40 results in spatial aliasing and thus would need additional constraints or prior information. Full article
(This article belongs to the Special Issue Geodesy for Gravity and Height Systems)
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21 pages, 8308 KiB  
Article
A Quasigeoid-Derived Transformation Model Accounting for Land Subsidence in the Mekong Delta towards Height System Unification in Vietnam
by Dinh Toan Vu, Sean Bruinsma, Sylvain Bonvalot, Dominique Remy and Georgios S. Vergos
Remote Sens. 2020, 12(5), 817; https://0-doi-org.brum.beds.ac.uk/10.3390/rs12050817 - 03 Mar 2020
Cited by 8 | Viewed by 3672
Abstract
A vertical offset model for Vietnam and its surrounding areas was determined based on the differences between height anomalies derived from 779 Global Navigation Satellite System (GNSS)/levelling points and those derived from a dedicated high-resolution gravimetric-only quasigeoid model called GEOID_LSC. First, the deterministic [...] Read more.
A vertical offset model for Vietnam and its surrounding areas was determined based on the differences between height anomalies derived from 779 Global Navigation Satellite System (GNSS)/levelling points and those derived from a dedicated high-resolution gravimetric-only quasigeoid model called GEOID_LSC. First, the deterministic transformation model to effectively fit the differences between the quasigeoid and GNSS/levelling heights was based on a third-order polynomial model. Second, the residual height anomalies have been interpolated to a grid employing Least-Squares Collocation. Finally, the distortions were restored to the residual grid. This model can be used for combination with a gravimetric quasigeoid model in GNSS levelling. The quality of GNSS/levelling data in Vietnam was analyzed and evaluated in this study. The annual subsidence rate from ALOS-1 was also used to analyze the effects of subsidence on the quality of GNSS/levelling data in the Mekong Delta. From this we made corrections to improve the accuracy of GNSS/levelling data in this region. The offset model was evaluated using cross-validation technique by comparing with GNSS/levelling data. Results indicate that the offset model has a standard deviation of 5.9 cm in the absolute sense. Based on this offset model, GNSS levelling can be carried out in most of Vietnam’s territory complying third-order levelling requirements, while the accuracy requirements for fourth-order levelling networks is met for the entire country. This model in combination with the developed gravimetric quasigeoid model should also contribute to the modernization of Vietnam’s height system. We also used high-quality GNSS/levelling data and the determined quasigeoid model to determine the geopotential value W0 for the Vietnam Local Vertical Datum. The gravity potential of the Vietnam Local Vertical Datum is estimated equal to W 0 LVD = 62,636,846.81 ± 0.70 m2s−2 with the global equipotential surface realized by the conventional value W0 = 62,636,853.4 m2s−2. Full article
(This article belongs to the Special Issue Geodesy for Gravity and Height Systems)
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23 pages, 13590 KiB  
Article
Performance Comparison of Geoid Refinement between XGM2016 and EGM2008 Based on the KTH and RCR Methods: Jilin Province, China
by Qiong Wu, Hongyao Wang, Bin Wang, Shengbo Chen and Hongqing Li
Remote Sens. 2020, 12(2), 324; https://0-doi-org.brum.beds.ac.uk/10.3390/rs12020324 - 18 Jan 2020
Cited by 5 | Viewed by 3572
Abstract
The selection of an appropriate global gravity field model and refinement method can effectively improve the accuracy of the refined regional geoid model in a certain research area. We analyzed the accuracy of Experimental Geopotential Model (XGM2016) based on the GPS-leveling data and [...] Read more.
The selection of an appropriate global gravity field model and refinement method can effectively improve the accuracy of the refined regional geoid model in a certain research area. We analyzed the accuracy of Experimental Geopotential Model (XGM2016) based on the GPS-leveling data and the modification parameters of the global mean square errors in the KTH geoid refinement in Jilin Province, China. The regional geoid was refined based on Earth Gravitational Model (EGM2008) and XGM2016 using both the Helmert condensation method with an RCR procedure and the KTH method. A comparison of the original two gravity field models to the GPS-leveling benchmarks showed that the accuracies of XGM2016 and EGM2008 in the plain area of Jilin Province are similar with a standard deviation (STD) of 5.8 cm, whereas the accuracy of EGM2008 in the high mountainous area is 1.4 cm better than that of XGM2016, which may be attributed to its low resolution. The modification parameters between the two gravity field models showed that the coefficient error of XGM2016 model was lower than that of EGM2008 for the same degree of expansion. The different modification limits and integral radii may produce a centimeter level difference in global mean square error, while the influence of the truncation error caused by the integral was at the millimeter level. The terrestrial gravity data error accounted for the majority of the global mean square error. The optimal least squares modification obtained the minimum global mean square error, and the global mean square error calculated based on XGM2016 model was reduced by about 1~3 cm compared with EGM2008. The refined geoid based on the two gravity field models indicated that both KTH and RCR method can effectively improve the STD of the geoid model from about six to three centimeters. The refined accuracy of EGM2008 model using RCR and KTH methods is slightly better than that of XGM2016 model in the plain and high mountain areas after seven-parameter fitting. EGM2008 based on the KTH method was the most precise at ± 2.0 cm in the plain area and ± 2.4 cm in the mountainous area. Generally, for the refined geoid based on the two Earth gravity models, KTH produced results similar to RCR in the plain area, and had relatively better performance for the mountainous area where terrestrial gravity data is sparse and unevenly distributed. Full article
(This article belongs to the Special Issue Geodesy for Gravity and Height Systems)
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11 pages, 49660 KiB  
Technical Note
Comparison of Marine Gravity Measurements from Shipborne and Satellite Altimetry in the Arctic Ocean
by Zilong Ling, Lihong Zhao, Tao Zhang, Guojun Zhai and Fanlin Yang
Remote Sens. 2022, 14(1), 41; https://0-doi-org.brum.beds.ac.uk/10.3390/rs14010041 - 23 Dec 2021
Cited by 5 | Viewed by 2809
Abstract
To understand the influence of sea ice on shipborne gravity measurements and the accuracy of the satellite-altimetry-derived gravity field in the Arctic Ocean, we compared shipborne gravity measurements with those obtained from satellite altimetric gravity measurements. The influence of sea ice on the [...] Read more.
To understand the influence of sea ice on shipborne gravity measurements and the accuracy of the satellite-altimetry-derived gravity field in the Arctic Ocean, we compared shipborne gravity measurements with those obtained from satellite altimetric gravity measurements. The influence of sea ice on the shipborne gravity measurements was mainly concentrated in the 0–6 km wavelength range, and the standard deviation of the noise amplitudes was 2.62 mGal. Compared to ice-free regions, the accuracies in the region with floating ice were reduced by 13% for DTU21 and 6% for SV31. Due to the influence of sea ice, satellite altimetric gravity data lose significant information in the 9–12 km wavelength range. The coherence curve of the shipborne gravity with bathymetry was nearly the same as that of the satellite altimetric gravity. The satellite data contain nearly all of the significant information that is present in the shipborne data. The differences between the shipborne and satellite gravity data are small and can be used to study the crustal structure of the Arctic. Full article
(This article belongs to the Special Issue Geodesy for Gravity and Height Systems)
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