Difference between revisions of "JSG T.35"

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(Created page with "<big>'''JSG 0.22: High resolution harmonic analysis and synthesis of potential fields'''</big> Chair: ''Sten Claessens (Australia)''<br> Affiliation:''Comm. 2 and GGOS'' __T...")
 
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<big>'''JSG 0.22: High resolution harmonic analysis and synthesis of potential fields'''</big>
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<big>'''JSG 0.22: Definition of next generation terrestrial reference frames'''</big>
  
Chair: ''Sten Claessens (Australia)''<br>
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Chair: ''Christopher Kotsakis (Greece)''<br>
Affiliation:''Comm. 2 and GGOS''
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Affiliation:''Comm. 1 and GGOS''
  
 
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===Terms of Reference===
 
===Terms of Reference===
  
The gravitational fields of the Earth and other celestial bodies in the Solar System are customarily represented by a series of spherical harmonic coefficients. The models made up of these harmonic coefficients are used widely in a large range of applications within geodesy. In addition, spherical harmonics are now used in many other areas of science such as geomagnetism, particle physics, planetary geophysics, biochemistry and computer graphics, but one of the first applications of spherical harmonics was related to the gravitational potential, and geodesists are still at the forefront of research into spherical harmonics. This holds true especially when it comes to the extension of spherical harmonic series to ever higher degree and order (d/o).
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A Terrestrial Reference Frame (TRF) is required for measuring the Earth orientation in space, for positioning objects at the Earth’s surface as well as satellites in orbit around the Earth, and for the analysis of geophysical processes and their spatiotemporal variations. TRFs are currently constructed by sets of tri-dimensional coordinates of ground stations, which implicitly realize the three orthogonal axes of the corresponding frame. To account for Earth’s deformations, these coordinates have been commonly modelled as piece-wise linear functions of time which are estimated from space geodetic data under various processing strategies, resulting to the usual type of geodetic frame solutions in terms of station coordinates (at some reference epoch) and constant velocities. Most recently, post-seismic deformation has been added as well in geodetic frame solutions. The requirements of the Earth science community for the accuracy level of such secular TRFs for present-day applications are in the order of 1 mm and 0.1 mm/year, which is not generally achievable at the present time. Improvements in data analysis models, coordinate variation models, optimal estimation procedures and datum definition choices (e.g. NNR conditions) should still be investigated in order to enhance the present positioning accuracy under the “linear” TRF framework.  
The maximum d/o of spherical harmonic series of the Earth’s gravitational potential has risen steadily over the past decades. The highest d/o models currently listed by the International Centre for Global Earth Models (ICGEM) have a maximum d/o of 2190. In recent years, spherical harmonic models of the topography and topographic potential to d/o 10,800 have been computed, and with ever-increasing computational prowess, expansions to even higher d/o are feasible. For comparison, the current highest-resolution global gravity model has a resolution of 7.2” in the space domain, which is roughly equivalent to d/o 90,000 in the frequency domain, while the highest-resolution global Digital Elevation Model has a resolution of 5 m, equivalent to d/o ~4,000,000.
 
  
The increasing maximum d/o of harmonic models has posed and continues to pose both theoretical and practical challenges for the geodetic community. For example, the computation of associated Legendre functions of the first kind, which are required for spherical harmonic analysis and synthesis, is traditionally subject to numerical instabilities and underflow/overflow problems. Much progress has been made on this issue by selection of suitable recurrence relations, summation strategies, and use of extended range arithmetic, but further improvements to efficiency may still be achieved.  
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Moreover, the consideration of seasonal changes in the station positions due to the effect of geophysical loading signals and other complex tectonic motions has created an additional interest towards the development of “non-linear” TRFs aiming to provide highly accurate coordinates of the quasi-instantaneous positions in a global network. This approach overcomes the limitation of global secular frames which model the average positions over a long time span, yet it creates significant new challenges and open problems that need to be resolved to meet the aforementioned accuracy requirements.
  
There are further separate challenges in ultra-high d/o harmonic analysis (the forward harmonic transform) and synthesis (the inverse harmonic transform). Many methods for the forward harmonic transform exist, typically separated into least-squares and quadrature methods, and further comparison between the two at high d/o, including studying the influence of aliasing, is of interest. The inverse harmonic transform, including synthesis of a large variety of quantities, has received much interest in recent years. In moving towards higher d/o series, highly efficient algorithms for synthesis on irregular surfaces and/or in scattered point locations, are of utmost importance.
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The above considerations provide the motivation for this JSG whose work will be focused to studying and improving the current approaches for the definition and realization of global TRFs from space geodetic data, in support of Earth mapping and monitoring applications. The principal aim is to identify the major issues causing the current internal/external accuracy limitations in global TRF solutions, and to investigate possible ways to overcome them either in the linear or the non-linear modeling framework.
 
 
Another question that has occupied geodesists for many decades is whether there is a substantial benefit to the use of oblate ellipsoidal (or spheroidal) harmonics instead of spherical harmonics.  The limitations of the spherical harmonic series for use on or near the Earth’s surface are becoming more and more apparent as the maximum d/o of the harmonic series increase. There are still open questions about the divergence effect and the amplification of the omission error in spherical and spheroidal harmonic series inside the Brillouin surface.
 
 
 
The Hotine-Jekeli transformation between spherical and spheroidal harmonic coefficients has proven very useful, in particular for spherical harmonic analysis of data on a reference ellipsoid. It has recently been improved upon and extended, while alternatives using surface spherical harmonics have also been proposed, but the performance of the transformations at very high d/o may be improved further. Direct use of spheroidal harmonic series requires (ratios of) associated Legendre functions of the second kind, and their stable and efficient computation is also of ongoing interest.
 
  
 
===Objectives===
 
===Objectives===
  
The objectives of this study group are to:
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* To review and compare from the theoretical point of view the current approaches for the definition and realization of global TRFs, including data reduction strategies and frame estimation methodologies.
* Create and compare stable and efficient methods for computation of ultra-high degree and order associated Legendre functions of the first and second kind (or ratios thereof), plus its derivatives and integrals.
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* To evaluate the distortion caused by hidden datum information within the unconstrained normal equations (NEQs) to combination solutions by the “minimum constraints” approach, and to develop efficient tools enforcing the appropriate rank deficiency in input NEQs when computing TRF solutions.
* Study the divergence effect of ultra-high degree spherical and spheroidal harmonic series inside the Brillouin sphere/spheroid.
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* To study the role of the 7/14-parameter Helmert transformation model in handling non-linear (non-secular) global frames, as well as to investigate the frame transformation problem in the presence of modeled seasonal variations in the respective coordinates.
* Verify the numerical performance of transformations between spherical and spheroidal harmonic coefficients to ultra-high degree and order.
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* To study theoretical and numerical aspects of the stacking problem, both at the NEQ level and at the coordinate time-series level, with unknown non-linear seasonal terms when estimating a global frame from space geodetic data.
* Compare least-squares and quadrature approaches to very high-degree and order spherical and spheroidal harmonic analysis.
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* To compare the aforementioned methodology with other alternative approaches in non-linear frame modeling, such as the computation of high-rate time series of global TRFs.
* Study efficient methods for ultra-high degree and order harmonic analysis (the forward harmonic transform) for a variety of data types and boundary surfaces.
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* To investigate the modeling choices for the datum definition in global TRFs with particular emphasis on the frame orientation and the different types of no-net-rotation (NNR) conditions.
* Study efficient methods for ultra-high degree and order harmonic synthesis (the inverse harmonic transform) of point values and area means of all potential quantities of interest on regular and irregular surfaces.
 
  
 
===Program of activities===
 
===Program of activities===
  
* Providing a platform for increased cooperation between group members, facilitating and encouraging exchange of ideas and research results.
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* Active participation at major geodetic meetings, promotion of related sessions at international scientific symposia and publication of important findings related to the JSG objectives.
* Creating and updating a bibliographic list of relevant publications from both the geodetic community as well as other disciplines for the perusal of group members.
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* Proposal for a state-of-art review paper in global frame theory, realization methodologies and open problems, co-authored by the JSG members.
* Organizing working meetings at international symposia and presenting research results in the appropriate sessions.
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* Organize a related session at the forthcoming Hotine-Marussi Symposium.
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* Launching a web page with emphasis on exchange of research ideas, recent results, updated bibliographic list of references and relevant publications from other disciplines.
  
 
===Membership===
 
===Membership===
  
'' '''Sten Claessens (Australia), chair''' <br /> Hussein Abd-Elmotaal (Egypt) <br /> Oleh Abrykosov (Germany) <br /> Blažej Bucha (Slovakia) <br /> Toshio Fukushima (Japan) <br /> Thomas Grombein (Germany) <br /> Christian Gruber (Germany) <br /> Eliška Hamáčková (Czech Republic) <br /> Christian Hirt (Germany) <br /> Christopher Jekeli (USA) <br /> Otakar Nesvadba (Czech Republic) <br /> Moritz Rexer (Germany) <br /> Josef Sebera (Czech Republic) <br /> Kurt Seitz (Germany) <br />''
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'' '''Christopher Kotsakis (Greece), chair''' <br /> Zuheir Altamimi (France) <br /> Michael Bevis (USA) <br /> Mathis Bloßfeld (Germany) <br /> David Coulot (France) <br /> Athanasios Dermanis (Greece) <br /> Richard Gross (USA) <br /> Tom Herring (USA) <br /> Michael Schindelegger (Austria) <br /> Manuela Seitz (Germany) <br /> Krzysztof Sośnica (Poland) <br />''

Revision as of 09:25, 29 April 2016

JSG 0.22: Definition of next generation terrestrial reference frames

Chair: Christopher Kotsakis (Greece)
Affiliation:Comm. 1 and GGOS

Terms of Reference

A Terrestrial Reference Frame (TRF) is required for measuring the Earth orientation in space, for positioning objects at the Earth’s surface as well as satellites in orbit around the Earth, and for the analysis of geophysical processes and their spatiotemporal variations. TRFs are currently constructed by sets of tri-dimensional coordinates of ground stations, which implicitly realize the three orthogonal axes of the corresponding frame. To account for Earth’s deformations, these coordinates have been commonly modelled as piece-wise linear functions of time which are estimated from space geodetic data under various processing strategies, resulting to the usual type of geodetic frame solutions in terms of station coordinates (at some reference epoch) and constant velocities. Most recently, post-seismic deformation has been added as well in geodetic frame solutions. The requirements of the Earth science community for the accuracy level of such secular TRFs for present-day applications are in the order of 1 mm and 0.1 mm/year, which is not generally achievable at the present time. Improvements in data analysis models, coordinate variation models, optimal estimation procedures and datum definition choices (e.g. NNR conditions) should still be investigated in order to enhance the present positioning accuracy under the “linear” TRF framework.

Moreover, the consideration of seasonal changes in the station positions due to the effect of geophysical loading signals and other complex tectonic motions has created an additional interest towards the development of “non-linear” TRFs aiming to provide highly accurate coordinates of the quasi-instantaneous positions in a global network. This approach overcomes the limitation of global secular frames which model the average positions over a long time span, yet it creates significant new challenges and open problems that need to be resolved to meet the aforementioned accuracy requirements.

The above considerations provide the motivation for this JSG whose work will be focused to studying and improving the current approaches for the definition and realization of global TRFs from space geodetic data, in support of Earth mapping and monitoring applications. The principal aim is to identify the major issues causing the current internal/external accuracy limitations in global TRF solutions, and to investigate possible ways to overcome them either in the linear or the non-linear modeling framework.

Objectives

  • To review and compare from the theoretical point of view the current approaches for the definition and realization of global TRFs, including data reduction strategies and frame estimation methodologies.
  • To evaluate the distortion caused by hidden datum information within the unconstrained normal equations (NEQs) to combination solutions by the “minimum constraints” approach, and to develop efficient tools enforcing the appropriate rank deficiency in input NEQs when computing TRF solutions.
  • To study the role of the 7/14-parameter Helmert transformation model in handling non-linear (non-secular) global frames, as well as to investigate the frame transformation problem in the presence of modeled seasonal variations in the respective coordinates.
  • To study theoretical and numerical aspects of the stacking problem, both at the NEQ level and at the coordinate time-series level, with unknown non-linear seasonal terms when estimating a global frame from space geodetic data.
  • To compare the aforementioned methodology with other alternative approaches in non-linear frame modeling, such as the computation of high-rate time series of global TRFs.
  • To investigate the modeling choices for the datum definition in global TRFs with particular emphasis on the frame orientation and the different types of no-net-rotation (NNR) conditions.

Program of activities

  • Active participation at major geodetic meetings, promotion of related sessions at international scientific symposia and publication of important findings related to the JSG objectives.
  • Proposal for a state-of-art review paper in global frame theory, realization methodologies and open problems, co-authored by the JSG members.
  • Organize a related session at the forthcoming Hotine-Marussi Symposium.
  • Launching a web page with emphasis on exchange of research ideas, recent results, updated bibliographic list of references and relevant publications from other disciplines.

Membership

Christopher Kotsakis (Greece), chair
Zuheir Altamimi (France)
Michael Bevis (USA)
Mathis Bloßfeld (Germany)
David Coulot (France)
Athanasios Dermanis (Greece)
Richard Gross (USA)
Tom Herring (USA)
Michael Schindelegger (Austria)
Manuela Seitz (Germany)
Krzysztof Sośnica (Poland)