Difference between pages "JSG T.28" and "JSG T.32"

From Icctwiki
(Difference between pages)
Jump to: navigation, search
(Created page with "<big>'''JSG 0.15: Regional geoid/quasi-geoid modelling – Theoretical framework for the sub-centimetre accuracy'''</big> Chairs: ''Jianliang Huang (Canada)''<br /> Affiliati...")
 
(Created page with "<big>'''JSG 0.19: High resolution harmonic analysis and synthesis of potential fields'''</big> Chair: ''Sten Claessens (Australia)''<br> Affiliation:''Comm. 2 and GGOS'' __T...")
 
Line 1: Line 1:
−
<big>'''JSG 0.15: Regional geoid/quasi-geoid modelling – Theoretical framework for the sub-centimetre accuracy'''</big>
+
<big>'''JSG 0.19: High resolution harmonic analysis and synthesis of potential fields'''</big>
  
−
Chairs: ''Jianliang Huang (Canada)''<br />
+
Chair: ''Sten Claessens (Australia)''<br>
−
Affiliation: ''Comm. 2 and GGOS''
+
Affiliation:''Comm. 2 and GGOS''
  
 
__TOC__
 
__TOC__
  
−
===Problem statement===
+
===Terms of Reference===
  
−
A theoretical framework for the regional geoid/quasi-geoid modelling is a conceptual structure to solve a geodetic boundary value problem regionally. It is a physically sound integration of a set of coherent definitions, physical models and constants, geodetic reference systems and mathematical equations. Current frameworks are designed to solve one of the two geodetic boundary value problems: Stokes’s and Molodensky’s. These frameworks were originally established and subsequently refined for many decades to get the best accuracy of the geoid/quasi-geoid model. The regional geoid/quasi-geoid model can now be determined with an accuracy of a few centimeters in a number of regions in the world, and has been adopted to define new vertical datum replacing the spirit-leveling networks in New Zealand and Canada. More and more countries are modernizing their existing height systems with the geoid-based datum. Yet the geoid model still needs further improvement to match the accuracy of the GNSS-based heightening. This requires the theory and its numerical realization, to be of sub-centimeter accuracy, and the availability of adequate data.
+
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).
 +
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.
  
−
Regional geoid/quasi-geoid modelling often involves the combination of satellite, airborne, terrestrial (shipborne and land) gravity data through the remove-compute-restore Stokes method and the least-squares collocation. Satellite gravity data from recent gravity missions (GRACE and GOCE) enable to model the geoid components with an accuracy of 1-2 cm at the spatial resolution of 100 km. Airborne gravity data are covering more regions with a variety of accuracies and spatial resolutions such as the US GRAV-D project. They often overlap with terrestrial gravity data, which are still unique in determining the high-degree geoid components. It can be foreseen that gravity data coverage will extend everywhere over lands, in particular, airborne data, in the near future.  Furthermore, the digital elevation models required for the gravity reduction have achieved global coverage with redundancy. A pressing question to answer is if these data are sufficiently accurate for the sub-centimeter geoid/quasi-geoid determination. This study group focuses on refining and establishing if necessary the theoretical frameworks of the sub-centimeter geoid/quasi-geoid.  
+
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.
 +
 
 +
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.
 +
 
 +
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 theoretical frameworks of the sub-centimeter geoid/quasi-geoid consist of, but are not limited to, the following components to study:
+
The objectives of this study group are to:
−
* Physical constant GM
+
* 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.
−
* W0 convention and changes
+
* Study the divergence effect of ultra-high degree spherical and spheroidal harmonic series inside the Brillouin sphere/spheroid.
−
* Geo-center convention and motion with respect to the International Terrestrial Reference Frame (ITRF)
+
* Verify the numerical performance of transformations between spherical and spheroidal harmonic coefficients to ultra-high degree and order.
−
* Geodetic Reference Systems
+
* Compare least-squares and quadrature approaches to very high-degree and order spherical and spheroidal harmonic analysis.
−
* Proper formulation of the geodetic boundary value problem
+
* Study efficient methods for ultra-high degree and order harmonic analysis (the forward harmonic transform) for a variety of data types and boundary surfaces.
−
* Nonlinear solution of the formulated geodetic boundary value problem
+
* 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.
−
* Data type, distribution and quality requirements
 
−
* Data interpolation and extrapolation methods
 
−
* Gravity reduction including downward or upward continuation from observation points down or up to the geoid, in particular over mountainous regions, polar glaciers and ice caps
 
−
* Anomalous topographic mass density effect on the geoid model
 
−
* Spectral combination of different types of gravity data
 
−
* Transformation between the geoid and quasi-geoid models
 
−
* The time-variable geoid/quasi-geoid change modelling
 
−
* Estimation of the geoid/quasi-geoid model inaccuracies
 
−
* Independent validation of geoid/quasi-geoid models
 
−
* Applications of new tools such as the radial basis functions
 
  
 
===Program of activities===
 
===Program of activities===
  
−
* The study group achieves its objectives through organizing splinter meetings in coincidence with major IAG conferences and workshops if possible.
+
* Providing a platform for increased cooperation between group members, facilitating and encouraging exchange of ideas and research results.
−
* Circulating and sharing progress reports, papers and presentations.
+
* 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.
−
* Presenting and publishing papers in the IAG symposia and scientific journals.  
+
* Organizing working meetings at international symposia and presenting research results in the appropriate sessions.
 +
 
 +
===Membership===
  
−
===Members===
+
'' '''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 />''
−
 
−
'' '''Jianliang Huang (Canada), chair''' <br /> '''Yan Ming Wang (USA), vice-chair''' <br /> Riccardo Barzaghi (Italy) <br /> Heiner Denker (Germany) <br /> Will Featherstone (Australia) <br /> René Forsberg (Denmark) <br /> Christian Gerlach (Germany) <br /> Christian Hirt (Germany) <br /> Urs Marti (Switzerland) <br /> Petr Vaníček (Canada) <br />''
 

Revision as of 10:03, 29 April 2016

JSG 0.19: High resolution harmonic analysis and synthesis of potential fields

Chair: Sten Claessens (Australia)
Affiliation:Comm. 2 and GGOS

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). 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.

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.

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

The objectives of this study group are to:

  • 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.
  • Study the divergence effect of ultra-high degree spherical and spheroidal harmonic series inside the Brillouin sphere/spheroid.
  • Verify the numerical performance of transformations between spherical and spheroidal harmonic coefficients to ultra-high degree and order.
  • Compare least-squares and quadrature approaches to very high-degree and order spherical and spheroidal harmonic analysis.
  • Study efficient methods for ultra-high degree and order harmonic analysis (the forward harmonic transform) for a variety of data types and boundary surfaces.
  • 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

  • Providing a platform for increased cooperation between group members, facilitating and encouraging exchange of ideas and research results.
  • 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.
  • Organizing working meetings at international symposia and presenting research results in the appropriate sessions.

Membership

Sten Claessens (Australia), chair
Hussein Abd-Elmotaal (Egypt)
Oleh Abrykosov (Germany)
Blažej Bucha (Slovakia)
Toshio Fukushima (Japan)
Thomas Grombein (Germany)
Christian Gruber (Germany)
Eliška Hamáčková (Czech Republic)
Christian Hirt (Germany)
Christopher Jekeli (USA)
Otakar Nesvadba (Czech Republic)
Moritz Rexer (Germany)
Josef Sebera (Czech Republic)
Kurt Seitz (Germany)

Retrieved from "http://icct.kma.zcu.cz/index.php?title=JSG_T.28&oldid=411"