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Geosciences
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Gravity Field Determination and Its Temporal Variation
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Gravity Field Determination and Its Temporal Variation

A special issue of Geosciences (ISSN 2076-3263). This special issue belongs to the section "Geophysics".

Deadline for manuscript submissions: closed (13 July 2018) | Viewed by 37919

Special Issue Editor

Prof. Dr. Mohammad Bagherbandi

E-Mail Website
Guest Editor
1. Division of Geodesy and Satellite Positioning, Royal Institute of Technology (KTH), SE-10044 Stockholm, Sweden
2. Faculty of Engineering and Sustainable Development, University of Gävle, SE-80176 Gävle, Sweden
Interests: geoid and gravity field; gravity field variation; height systems; mass transportation; quasi-geoid; reference system
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

It is my pleasure to inform you that Geosciences has decided to publish a Special Issue on "Gravity Field Determination and Its Temporal Variations". Hereby, we would like to invite you to contribute to this issue by submitting a scientific paper.

Global and local gravity field modeling is very important for various applications in geodesy, geodynamics, and geophysics. For this purpose, input data are satellite-based data, especially those from dedicated space missions, e.g., GRACE (Gravity Recovery and Climate Experiment), GOCE (Gravity field and steady-state Ocean Circulation Explorer), future satellite missions, satellite altimetry, terrestrial and air-borne gravimetry, and shipborne data. Static gravity field models are vital for the unification of height systems in order to determine an accurate international height reference system, sea level rise, and mean dynamic topography modeling, and also in combination with geophysical models for lithospheric structure modeling (e.g., the determination of crustal thickness).

The monitoring of temporal gravity changes is important for updating the static geoid/gravity field model. The change in the gravity field, over time, is caused by the redistribution of masses within the Earth. Temporal changes in the gravity field over many years of monthly repeated data from the satellite mission, particularly the Gravity Recovery and Climate Experiment (GRACE), are used to demonstrate their power in determining large-scale Earth mass and geoid changes, such as positive geoid height rates in Laurentia and Fennoscandia related to glacial isostatic adjustments, and negative rates in Greenland and West Antarctica, as a result of mass losses due to ice-sheet melting. Furthermore, various initiatives are ongoing to prepare for future gravity missions, the most promising of which is the GRACE follow-on mission in 2018.  Therefore, we would like to invite you to submit articles regarding your recent work, experimental research, or case studies, on the above and/or following topics:

  • Global static gravity field models (assessments, methodological development, uncertainties and applications)
  • Local and regional high-resolution gravity/geoid models
  • Datum unification and international height reference system
  • Geodetic gravity network developments
  • Boundary-value problem in physical geodesy, no-topography gravity anomaly, topographic bias, terrain correction and atmospheric effect for determining geoid,     least-square modification of Stokes formula
  • Temporal variation of gravity field, mass transportation and its application, such as climate change and ground surface deformation using satellite gravimetry missions
  • Future time varying gravity field missions, e.g., GRACE follow-on mission (simulations    and assessments).

Please let us know if you intend to send an article by sending us a short abstract, outlining the purpose of the research and the principal results obtained, in order to verify (at an early stage) if the contribution you intend to submit fits with the objectives of the Special Issue. The tentative outline of your work (i.e., Title, Authors, Affiliations, and Abstract) should be sent to [email protected], which in its final form should be submitted by 13 July 2018.

Prof. Mohammad Bagherbandi
Guest Editor

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. Geosciences is an international peer-reviewed open access monthly 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 1800 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

  • Geoid and gravity field
  • Gravity field variations
  • Height systems
  • Mass transportation
  • Quasi-geoid
  • Reference system

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Published Papers (8 papers)

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Research

15 pages, 3608 KiB  
Article
Assessment of Earth Gravity Field Models in the Medium to High Frequency Spectrum Based on GRACE and GOCE Dynamic Orbit Analysis
by Thomas D. Papanikolaou and Dimitrios Tsoulis
Geosciences 2018, 8(12), 441; https://doi.org/10.3390/geosciences8120441 - 27 Nov 2018
Cited by 5 | Viewed by 3825
Abstract
An analysis of current static and time-variable gravity field models is presented focusing on the medium to high frequencies of the geopotential as expressed by the spherical harmonic coefficients. A validation scheme of the gravity field models is implemented based on dynamic orbit [...] Read more.
An analysis of current static and time-variable gravity field models is presented focusing on the medium to high frequencies of the geopotential as expressed by the spherical harmonic coefficients. A validation scheme of the gravity field models is implemented based on dynamic orbit determination that is applied in a degree-wise cumulative sense of the individual spherical harmonics. The approach is applied to real data of the Gravity Field and Steady-State Ocean Circulation (GOCE) and Gravity Recovery and Climate Experiment (GRACE) satellite missions, as well as to GRACE inter-satellite K-band ranging (KBR) data. Since the proposed scheme aims at capturing gravitational discrepancies, we consider a few deterministic empirical parameters in order to avoid absorbing part of the gravity signal that may be included in the monitored orbit residuals. The present contribution aims at a band-limited analysis for identifying characteristic degree ranges and thresholds of the various GRACE- and GOCE-based gravity field models. The degree range 100–180 is investigated based on the degree-wise cumulative approach. The identified degree thresholds have values of 130 and 160 based on the GRACE KBR data and the GOCE orbit analysis, respectively. Full article
(This article belongs to the Special Issue Gravity Field Determination and Its Temporal Variation)
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13 pages, 4262 KiB  
Article
Application of Radial Basis Functions for Height Datum Unification
by Ismael Foroughi, Abdolreza Safari, Pavel Novák and Marcelo C. Santos
Geosciences 2018, 8(10), 369; https://doi.org/10.3390/geosciences8100369 - 2 Oct 2018
Cited by 8 | Viewed by 3744
Abstract
Local gravity field modelling demands high-quality gravity data as well as an appropriate mathematical model. Particularly in coastal areas, there may be different types of gravity observations available, for instance, terrestrial, aerial, marine gravity, and satellite altimetry data. Thus, it is important to [...] Read more.
Local gravity field modelling demands high-quality gravity data as well as an appropriate mathematical model. Particularly in coastal areas, there may be different types of gravity observations available, for instance, terrestrial, aerial, marine gravity, and satellite altimetry data. Thus, it is important to develop a proper tool to merge the different data types for local gravity field modelling and determination of the geoid. In this study, radial basis functions, as a commonly useful tool for gravity data integration, are employed to model the gravity potential field of the southern part of Iran using terrestrial gravity anomalies, gravity anomalies derived from re-tracked satellite altimetry, marine gravity anomalies, and gravity anomalies synthesized from an Earth gravity model. Reference GNSS/levelling (geometric) geoidal heights are used to evaluate the accuracy of the estimated local gravity field model. The gravimetric geoidal heights are in acceptable agreement with the geometric ones in terms of the standard deviation and the mean value which are 4.1 and 12 cm, respectively. Besides, the reference benchmark of the national first-order levelling network of Iran is located in the study area. The derived gravity model was used to compute the gravity potential difference at this point and then transformed into a height difference which results in the value of the shift of this benchmark with respect to the geoid. The estimated shift shows a good agreement with previously published studies. Full article
(This article belongs to the Special Issue Gravity Field Determination and Its Temporal Variation)
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16 pages, 926 KiB  
Article
GRACETOOLS—GRACE Gravity Field Recovery Tools
by Neda Darbeheshti, Florian Wöske, Matthias Weigelt, Christopher Mccullough and Hu Wu
Geosciences 2018, 8(9), 350; https://doi.org/10.3390/geosciences8090350 - 15 Sep 2018
Cited by 2 | Viewed by 5528
Abstract
This paper introduces GRACETOOLS, the first open source gravity field recovery tool using GRACE type satellite observations. Our aim is to initiate an open source GRACE data analysis platform, where the existing algorithms and codes for working with GRACE data are shared and [...] Read more.
This paper introduces GRACETOOLS, the first open source gravity field recovery tool using GRACE type satellite observations. Our aim is to initiate an open source GRACE data analysis platform, where the existing algorithms and codes for working with GRACE data are shared and improved. We describe the first release of GRACETOOLS that includes solving variational equations for gravity field recovery using GRACE range rate observations. All mathematical models are presented in a matrix format, with emphasis on state transition matrix, followed by details of the batch least squares algorithm. At the end, we demonstrate how GRACETOOLS works with simulated GRACE type observations. The first release of GRACETOOLS consist of all MATLAB M-files and is publicly available at Supplementary Materials. Full article
(This article belongs to the Special Issue Gravity Field Determination and Its Temporal Variation)
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16 pages, 3586 KiB  
Article
Decorrelation of GRACE Time Variable Gravity Field Solutions Using Full Covariance Information
by Alexander Horvath, Michael Murböck, Roland Pail and Martin Horwath
Geosciences 2018, 8(9), 323; https://doi.org/10.3390/geosciences8090323 - 29 Aug 2018
Cited by 29 | Viewed by 5667
Abstract
In this study the feasibility and performance of time variable decorrelation (VADER) filters derived from covariance information on decadal Gravity Recovery and Climate Experiment (GRACE) time series are investigated. The VADER filter is based on publicly available data that are provided by several [...] Read more.
In this study the feasibility and performance of time variable decorrelation (VADER) filters derived from covariance information on decadal Gravity Recovery and Climate Experiment (GRACE) time series are investigated. The VADER filter is based on publicly available data that are provided by several GRACE processing centers, and does not need its own Level-2 processing chain. Numerical closed loop simulations, incorporating stochastic and deterministic error budgets, serve as basis for the design of the filter setup, and the resulting filters are subsequently applied for real data processing. The closed loop experiments demonstrate the impact of temporally varying error and signal covariance matrices that are used for the design of decorrelation filters. The results indicate an average reduction of cumulative geoid height errors of 15% using time-variable instead of static decorrelation. Based on the simulation experience, a real data filtering procedure is designed and set up. It is applied to the ITSG-Grace2014 time variable gravity field time series with its associated full monthly covariance matrices. To assess the validity of the approach, linear mass trend estimates for the Antarctic Peninsula are computed using VADER filters and compared to previous estimates from both, GRACE and other mass balance estimation techniques. The mass change results obtained show very good agreement with other estimates and are robust against variations of the filter strength. The DDK decorrelation filter serves as main benchmark for the assessment of the VADER filter. For comparable filter strengths the VADER filters achieve a better de-striping and deliver smaller formal errors than static filters like the DDK. Full article
(This article belongs to the Special Issue Gravity Field Determination and Its Temporal Variation)
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30 pages, 7875 KiB  
Article
Impact of Groundtrack Pattern of a Single Pair Mission on the Gravity Recovery Quality
by Siavash Iran-Pour, Matthias Weigelt, Alireza Amiri-Simkooei and Nico Sneeuw
Geosciences 2018, 8(9), 315; https://doi.org/10.3390/geosciences8090315 - 23 Aug 2018
Cited by 1 | Viewed by 3113
Abstract
For future gravity satellite missions, aliasing of high frequency geophysical signals into the lower frequencies is one of the most challenging obstacles to recovering true gravity signals, i.e., to recover the truth. Several studies have investigated the impact of satellite groundtrack pattern on [...] Read more.
For future gravity satellite missions, aliasing of high frequency geophysical signals into the lower frequencies is one of the most challenging obstacles to recovering true gravity signals, i.e., to recover the truth. Several studies have investigated the impact of satellite groundtrack pattern on the quality of gravity recovery. Among those works, the concept of sub-cycle has been discussed as well. However, most of that research has focused on the impact of sampling patterns on global solutions up to a fixed maximum spherical harmonic coefficient, rather than the associated coefficient defined by the Colombo-Nyquist and modified Colombo-Nyquist rules. This work tries to look more closely into the influence of sampling patterns on the gravity recovery quality for global and regional studies when the Colombo-Nyquist and modified Colombo-Nyquist rules apply. For the regional study, the impact of groundtrack patterns of different satellite constellation scenarios are investigated for a hydrological basin in central Africa. The quality of the gravity products are assessed by different metrics, e.g., by spatial covariance representation. The potential meaning of the sub-cycle concept in terms of global and local impacts is also investigated by different repeat-orbit scenarios with even and odd parities. Different solution scenarios in terms of the original and modified Colombo-Nyquist rules will be discussed. The results of our study emphasize the impact of maximum harmonics of the recovery, the influence of sub-cycle on the local gravity recovery and the mission formation impact on the recovery error. Full article
(This article belongs to the Special Issue Gravity Field Determination and Its Temporal Variation)
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10 pages, 1960 KiB  
Article
A New Tool for Airborne Gravimetry Survey Simulation
by Daniele Sampietro, Ahmed Hamdi Mansi and Martina Capponi
Geosciences 2018, 8(8), 292; https://doi.org/10.3390/geosciences8080292 - 6 Aug 2018
Cited by 8 | Viewed by 5655
Abstract
Airborne gravimetry represents nowadays probably the most efficient technique to collect gravity observations close to the Earth’s surface. In the 1990s, thanks to the development of the Global Navigation Satellite Systems (GNSS), which has made accurate navigational data available, this technique started to [...] Read more.
Airborne gravimetry represents nowadays probably the most efficient technique to collect gravity observations close to the Earth’s surface. In the 1990s, thanks to the development of the Global Navigation Satellite Systems (GNSS), which has made accurate navigational data available, this technique started to spread worldwide because of its capability to provide measurements in a fast and cost-effective way. Differently from other techniques such as shipborne gravimetry, it has the advantage to provide gravity measurements also in challenging environments which can be difficult to access otherwise, like mountainous areas, rain forests and polar regions. For such reasons, airborne gravimetry is used for various applications related to the regional gravity field modelling: from the computation of high accurate local geoid for geodetic applications to geophysical ones, specifically related to oil and gas exploration activities or more in general for regional geological studies. Depending on the different kinds of application and the final required accuracy, the definition of the main characteristics of the airborne survey, e.g., the planar distance between consecutive flight tracks, the aircraft velocity, etc., can be a difficult task. In this work, we present a new software package, which would help in properly accomplishing the survey design task. Basically, the developed software solution allows for generating a realistic (from the observation noise point of view) gravimetric signal, and, after that, to predict the accuracy and spatial resolution of the final retrievable gravimetric field, in terms of gravity disturbances, given the flight main characteristics. The proposed procedure is suited for airborne survey planning in order to be able to optimize the design of the survey according to the required final accuracy. With the aim to evaluate the influence of the various survey parameters on the expected accuracy of the airborne survey, different numerical tests have been performed on simulated and real datasets. For instance, it has been shown that if the observation noise is not properly modeled in the data filtering step, the survey results degrade about 25%, while not acquiring control lines during the survey will basically reduce the final accuracy by a factor of two. Full article
(This article belongs to the Special Issue Gravity Field Determination and Its Temporal Variation)
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Graphical abstract

10 pages, 2884 KiB  
Article
On the Applicability of Molodensky’s Concept of Heights in Planetary Sciences
by Robert Tenzer and Ismael Foroughi
Geosciences 2018, 8(7), 239; https://doi.org/10.3390/geosciences8070239 - 29 Jun 2018
Cited by 2 | Viewed by 3900
Abstract
Geometric heights, defined with respect to a geometric reference surface, are the most commonly used in planetary studies, but the use of physical heights defined with respect to an equipotential surface (typically the geoid) has been also acknowledged for specific studies (such as [...] Read more.
Geometric heights, defined with respect to a geometric reference surface, are the most commonly used in planetary studies, but the use of physical heights defined with respect to an equipotential surface (typically the geoid) has been also acknowledged for specific studies (such as gravity-driven mass movements). In terrestrial studies, the geoid is defined as an equipotential surface that best fits the mean sea surface and extends under continents. Since gravimetric geoid modelling under continents is limited by the knowledge of a topographic density distribution, alternative concepts have been proposed. Molodensky introduced the quasigeoid as a height reference surface that could be determined from observed gravity without adopting any hypothesis about the topographic density. This concept is widely used in geodetic applications because differences between the geoid and the quasigeoid are mostly up to a few centimeters, except for mountainous regions. Here we discuss the possible applicability of Molodensky’s concept in planetary studies. The motivation behind this is rationalized by two factors. Firstly, knowledge of the crustal densities of planetary bodies is insufficient. Secondly, large parts of planetary surfaces have negative heights, implying that density information is not required. Taking into consideration the various theoretical and practical aspects discussed in this article, we believe that the choice between the geoid and the quasigeoid is not strictly limited because both options have advantages and disadvantages. We also demonstrate differences between the geoid and the quasigeoid on Mercury, Venus, Mars and Moon, showing that they are larger than on Earth. Full article
(This article belongs to the Special Issue Gravity Field Determination and Its Temporal Variation)
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8 pages, 254 KiB  
Article
Topographic Effects in Geoid Determinations
by Lars E. Sjöberg
Geosciences 2018, 8(4), 143; https://doi.org/10.3390/geosciences8040143 - 23 Apr 2018
Cited by 8 | Viewed by 5065
Abstract
Traditionally, geoid determination is applied by Stokes’ formula with gravity anomalies after removal of the attraction of the topography by a simple or refined Bouguer correction, and restoration of topography by the primary indirect topographic effect (PITE) after integration. This technique leads to [...] Read more.
Traditionally, geoid determination is applied by Stokes’ formula with gravity anomalies after removal of the attraction of the topography by a simple or refined Bouguer correction, and restoration of topography by the primary indirect topographic effect (PITE) after integration. This technique leads to an error of the order of the quasigeoid-to-geoid separation, which is mainly due to an incomplete downward continuation of gravity from the surface to the geoid. Alternatively, one may start from the modern surface gravity anomaly and apply the direct topographic effect on the anomaly, yielding the no-topography gravity anomaly. After downward continuation of this anomaly to sea-level and Stokes integration, a theoretically correct geoid height is obtained after the restoration of the topography by the PITE. The difference between the Bouguer and no-topography gravity anomalies (on the geoid or in space) is the “secondary indirect topographic effect”, which is a necessary correction in removing all topographic signals. In modern applications of an Earth gravitational model (EGM) in geoid determination a topographic correction is also needed in continental regions. Without the correction the error can range to a few metres in the highest mountains. The remove-compute-restore and Royal Institute of Technology (KTH) techniques for geoid determinations usually employ a combination of Stokes’ formula and an EGM. Both techniques require direct and indirect topographic corrections, but in the latter method these corrections are merged as a combined topographic effect on the geoid height. Finally, we consider that any uncertainty in the topographic density distribution leads to the same error in gravimetric and geometric geoid estimates, deteriorating GNSS-levelling as a tool for validating the topographic mass distribution correction in a gravimetric geoid model. Full article
(This article belongs to the Special Issue Gravity Field Determination and Its Temporal Variation)
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