Difference between revisions of "JSG T.38"

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<big>'''JSG T.23: Spherical and spheroidal integral formulas of the potential theory for transforming classical and new gravitational observables'''</big>
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<big>'''JSG T.38: Exploring the similarities and dissimilarities among different geoid/quasigeoid modelling techniques in view of cm-precise and cm-accurate geoid/quasigeoid'''</big>
  
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Chair: ''Michal Šprlák (Czech Republic)''<br>
+
Chair: ''Ropesh Goyal (India)''<br>
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Affiliation:''Commission 2 and GGOS''
+
Vice-Chair: ''Sten Classens (Australia)''<br>
 +
Affiliations: ''Commission 2, IGFS''
  
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__TOC__
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===Terms of Reference===
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<nowiki>Insert non-formatted text here</nowiki>
 
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===Introduction===
 
  
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The gravitational field represents one of the principal properties of any planetary body. Physical quantities, e.g., the gravitational potential or its gradients (components of gravitational tensors), describe gravitational effects of any mass body. They help indirectly in sensing inner structures of planets and their (sub-)surface processes. Thus, they represent an indispensable tool for understanding inner structures and processes of planetary bodies and for solving challenging problems in geodesy, geophysics and other planetary sciences.
+
It is over 170 years since George Gabriel Stokes published his seminal formula for
 +
geoid determination using gravity anomalies. The formula was derived in spherical
 +
approximation and is valid under some well-known assumptions. Since then, geoid
 +
modelling has revolved more or less around handling these assumptions. As a result,
 +
there are now various geoid and quasigeoid computation methods of both types, i.e.,
 +
methods with and without requiring the Stokes integration. However, despite this
 +
long-elapsed time, the determination of a cm-precise and/or cm-accurate geoid and
 +
quasigeoid remains an ongoing quest, although it has been achieved in a few studies. <br />
  
−
Various measurement principles have been developed for collecting gravitational data by terrestrial, marine, airborne or satellite sensors. From a theoretical point of view, different parameterizations of the gravitational field have been introduced. To transform observable parameters into sought parameters, various methods have been introduced, e.g., boundary-value problems of the potential theory have been formulated and solved analytically by integral transformations.
+
With the computation of cm-precise and/or cm-accurate geoid, a supposition can
 +
be formed that solutions from different geoid modelling methods should converge
 +
within a given threshold, with an ideal threshold value being one-cm. The rationale is
 +
that, for a region, all the methods can be used to calculate the geoid using the same
 +
data and underlying theory. Still, methods differ primarily due to different handling
 +
of the data, and assumptions and approximations. Different methods provide different
 +
solutions due to many aspects including but not limited to: 1. different modifications
 +
of Stokes’s kernel, 2. different prediction/interpolation/extrapolation methods for
 +
non-Stokes integrating geoid modelling methods, 3. use of geodetic versus geocentric
 +
coordinates, 4. different Global Geopotential Models, 5. different gridding and merging
 +
techniques, 6. different parameter sweeps (integration radius and kernel modification
 +
degree), and 7. different handling of topography, atmosphere, spherical approximation,
 +
and downward continuation. <br />
  
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Transforms based on solving integral equations of Stokes, Vening-Meinesz and Hotine have traditionally been of significant interest in geodesy as they accommodated gravity field observables in the past. However, new gravitational data have recently become available with the advent of satellite-to-satellite tracking, Doppler tracking, satellite altimetry, satellite gravimetry, satellite gradiometry and chronometry. Moreover, gravitational curvatures have already been measured in laboratory. New observation techniques have stimulated formulations of new boundary-value problems, equally as possible considerations on a tie to partial differential equations of the second order on a two-dimensional manifold. Consequently, the family of surface integral formulas has considerably extended, covering now mutual transformations of gravitational gradients of up to the third order.
+
Given these possible sources for differences in geoid models, it becomes inevitable
 +
to first create a rigorous definition of a “cm-precise” and “cm-accurate” geoid followed
 +
by a comparative study of intermediate steps of different geoid modelling methods,
 +
in addition to comparing only the final results from different methods separately.
 +
Comparative study of intermediate steps is essential given the fact that if using the
 +
same datasets in different methods, it is expected to have geoid differences less than
 +
one cm when the methods are designed to take into account all effects greater than
 +
one cm. <br />
  
−
In light of numerous efforts in extending the apparatus of integral transforms, many theoretical and numerical issues still remain open. Within this JSG, open theoretical questions related to existing surface integral formulas, such as stochastic modelling, spectral combining of various gradients and assessing numerical accuracy, will be addressed. We also focus on extending the apparatus of spheroidal integral transforms which is particularly important for modelling gravitational fields of oblate or prolate planetary bodies.
+
Further, in view of cm-precise and/or cm-accurate geoid, it is important to compare
 +
multiple methods and parameter sweeps in different areas. This is because it would
 +
form an ideal strategy for a consistently precise/accurate geoid model. The difference
 +
between the precise geoid and consistently precise geoid is that the precision, in the
 +
latter, should be preserved when a geoid model is validated region-wise in addition to
 +
the validation with the complete ground truth. Otherwise, cm-precise geoid may have
 +
limited meaning.
  
 
===Objectives===
 
===Objectives===
  
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* Study noise propagation through spherical and spheroidal integral transforms.
+
• Develop a statistical definition of cm-precise and cm-accurate geoid/quasi-geoid. <br />
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* Propose efficient numerical algorithms for precise evaluation of spherical and spheroidal integral transformations.
+
• Study and quantify the differences in handling the topography, atmosphere,
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* Develop mathematical expressions for calculating the distant-zone effects for spherical and spheroidal integral transformations.
+
ellipsoidal correction, and downward continuation in different geoid/quasigeoid
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* Study mathematical properties of differential operators in spheroidal coordinates which relate various functionals of the gravitational potential.
+
modelling methods. <br />
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* Formulate and solve spheroidal gradiometric and spheroidal curvature boundary-value problems.
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• Study, quantify and reduce the assumptions and approximations in different geoid
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* Complete the family of spheroidal integral transforms among various types of gravitational gradients and to derive corresponding integral kernel functions.
+
modelling methods to attain congruency within some threshold. <br />
−
* Investigate optimal combination techniques of various gravitational gradients for gravitational field modelling at all scales.
+
• Study the requirement for merging various components/steps of different geoid
 +
modelling methods. <br />
 +
• Develop external validation techniques to determine region- or nationwide
  
 
===Program of activities===
 
===Program of activities===
  
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* Presenting findings at international geodetic or geophysical conferences, meetings and workshops.
+
• Presenting research findings at major international geodetic conferences, meetings,
−
* Interacting with IAG Commissions and GGOS.
+
and workshops. <br />
−
* Monitoring research activities of JSG members and other scientists whose research interests are related to scopes of this JSG.
+
• Preparation of joint publications with JSG members. <br />
−
* Organizing a session at the Hotine-Marussi Symposium 2022.
+
• Organizing a session at the Hotine-Marussi Symposium 2026. <br />
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* Providing a bibliographic list of publications from different branches of the science relevance to scopes of this JSG.
+
• Organizing splinter meetings at major international conferences and a series of online
 +
workshop. <br />
 +
• Supporting and cooperating with IAG commissions, services, and other study and
 +
working groups on gravity modelling and height systems.
  
 
===Members===
 
===Members===
  
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'' '''Michal Šprlák (Czech Republic), chair''' <br /> Sten Claessens (Australia) <br /> Mehdi Eshagh (Sweden) <br /> Ismael Foroughi (Canada) <br /> Peter Holota (Czech Republic) <br /> Juraj Janák (Slovakia) <br /> Otakar Nesvadba (Czech Republic) <br /> Pavel Novák (Czech Republic) <br /> Vegard Ophaug (Norway) <br /> Martin Pitoňák (Czech Republic) <br /> Michael Sheng (Canada) <br /> Natthachet Tangdamrongsub (USA) <br /> Robert Tenzer (Hong Kong) <br />''
+
Ropesh Goyal (India); Chair <br />
 +
Sten Claessens (Australia); Vice-Chair <br />  
 +
Ismael Foroughi (Canada) <br />  
 +
Jonas Ågren (Sweden) <br />  
 +
Xiaopeng Li (USA) <br />  
 +
Bihter Erol (Turkey) <br />  
 +
Jack McCubbine (Australia) <br />  
 +
Pavel Novák (Czech Republic) <br />  
 +
Koji Matsuo (Japan) <br />
 +
Riccardo Barzaghi (Italy) <br />  
 +
Michal Šprlák (Czech Republic) <br />  
 +
Jianliang Huang (Canada) <br />  
 +
Yan-Ming Wang (USA) <br />  
 +
Cheinway Hwang (China-Taipei) <br />
 +
Neda Darbeheshti (Australia) <br />
  
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===Bibliography===
+
===Associate Members===
 +
 
 +
Jack McCubbine (Australia) <br />

Latest revision as of 01:30, 1 September 2024

JSG T.38: Exploring the similarities and dissimilarities among different geoid/quasigeoid modelling techniques in view of cm-precise and cm-accurate geoid/quasigeoid

Chair: Ropesh Goyal (India)
Vice-Chair: Sten Classens (Australia)
Affiliations: Commission 2, IGFS

Terms of Reference

It is over 170 years since George Gabriel Stokes published his seminal formula for geoid determination using gravity anomalies. The formula was derived in spherical approximation and is valid under some well-known assumptions. Since then, geoid modelling has revolved more or less around handling these assumptions. As a result, there are now various geoid and quasigeoid computation methods of both types, i.e., methods with and without requiring the Stokes integration. However, despite this long-elapsed time, the determination of a cm-precise and/or cm-accurate geoid and quasigeoid remains an ongoing quest, although it has been achieved in a few studies.

With the computation of cm-precise and/or cm-accurate geoid, a supposition can be formed that solutions from different geoid modelling methods should converge within a given threshold, with an ideal threshold value being one-cm. The rationale is that, for a region, all the methods can be used to calculate the geoid using the same data and underlying theory. Still, methods differ primarily due to different handling of the data, and assumptions and approximations. Different methods provide different solutions due to many aspects including but not limited to: 1. different modifications of Stokes’s kernel, 2. different prediction/interpolation/extrapolation methods for non-Stokes integrating geoid modelling methods, 3. use of geodetic versus geocentric coordinates, 4. different Global Geopotential Models, 5. different gridding and merging techniques, 6. different parameter sweeps (integration radius and kernel modification degree), and 7. different handling of topography, atmosphere, spherical approximation, and downward continuation.

Given these possible sources for differences in geoid models, it becomes inevitable to first create a rigorous definition of a “cm-precise” and “cm-accurate” geoid followed by a comparative study of intermediate steps of different geoid modelling methods, in addition to comparing only the final results from different methods separately. Comparative study of intermediate steps is essential given the fact that if using the same datasets in different methods, it is expected to have geoid differences less than one cm when the methods are designed to take into account all effects greater than one cm.

Further, in view of cm-precise and/or cm-accurate geoid, it is important to compare multiple methods and parameter sweeps in different areas. This is because it would form an ideal strategy for a consistently precise/accurate geoid model. The difference between the precise geoid and consistently precise geoid is that the precision, in the latter, should be preserved when a geoid model is validated region-wise in addition to the validation with the complete ground truth. Otherwise, cm-precise geoid may have limited meaning.

Objectives

• Develop a statistical definition of cm-precise and cm-accurate geoid/quasi-geoid.
• Study and quantify the differences in handling the topography, atmosphere, ellipsoidal correction, and downward continuation in different geoid/quasigeoid modelling methods.
• Study, quantify and reduce the assumptions and approximations in different geoid modelling methods to attain congruency within some threshold.
• Study the requirement for merging various components/steps of different geoid modelling methods.
• Develop external validation techniques to determine region- or nationwide

Program of activities

• Presenting research findings at major international geodetic conferences, meetings, and workshops.
• Preparation of joint publications with JSG members.
• Organizing a session at the Hotine-Marussi Symposium 2026.
• Organizing splinter meetings at major international conferences and a series of online workshop.
• Supporting and cooperating with IAG commissions, services, and other study and working groups on gravity modelling and height systems.

Members

Ropesh Goyal (India); Chair
Sten Claessens (Australia); Vice-Chair
Ismael Foroughi (Canada)
Jonas Ågren (Sweden)
Xiaopeng Li (USA)
Bihter Erol (Turkey)
Jack McCubbine (Australia)
Pavel Novák (Czech Republic)
Koji Matsuo (Japan)
Riccardo Barzaghi (Italy)
Michal Šprlák (Czech Republic)
Jianliang Huang (Canada)
Yan-Ming Wang (USA)
Cheinway Hwang (China-Taipei)
Neda Darbeheshti (Australia)

Associate Members

Jack McCubbine (Australia)

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