Difference between revisions of "IC SG9"

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<big>'''Application of time-series analysis in geodesy'''</big>
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<big>'''JSG 0.18: High resolution harmonic analysis and synthesis of potential fields'''</big>
  
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Chair: ''W. Kosek (Poland)''<br>
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Chair: ''Sten Claessens (Australia)''<br>
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Affiliation:''Comm. 1, 2, 3, 4''
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Affiliation:''Comm. 2 and GGOS''
  
 
__TOC__
 
__TOC__
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===Introduction===
 
  
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Observations of the new space geodetic techniques deliver a global picture of dynamics of the Earth usually represented in the form of the time series which describe 1) changes of the surface geometry of the Earth due to horizontal and vertical deformations of the land surface, variations in the ocean surface and ice covers 2) the fluctuations in the orientation of the Earth divided into precession, nutation, polar motion and spin rate, and, 3) the variations of the Earth’s gravitational field expressed as gravity or geoid anomalies as well as the variations of the centre of mass of the Earth. The temporal variations of Earth rotation and gravity/geoid represent the total, integral effect of all mass exchange  between all elements of  Earth’s system including atmosphere, ocean and hydrology.
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===Terms of Reference===
  
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Different time series analysis methods are applied to analyze all these geodetic time series for better understanding of the relation between all elements of the Earth’s system as well as their geophysical causes. The interactions between different components of the Earth’s system are very complex so the nature of considered signals in the geodetic time series is mostly wideband, irregular and non stationary. Thus, it is necessary to apply time frequency analysis methods in order to analyze these time series in different frequency bands as well as to explain their relations to geophysical processes e.g. by computing time frequency coherence between Earth’s rotation or the gravity field data and data representing the mass exchange between the atmosphere, ocean and hydrology.
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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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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.
  
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Other geodetic time series may include for example variations of site positions, tropospheric  delay, ionospheric electron content, temporal variations of estimated orbit parameters. Time series analysis methods can be also applied to analyze data on the surface including maps of the gravity field, sea level and ionosphere as well as temporal variations of such surface data. The main problems to deal with concern estimation of deterministic (including trend and periodic variations) and stochastic (non periodic variations and random changes) components of the geodetic time series as well as application of digital filters for extracting components with chosen frequency bandwidth.
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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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For coping with small geodetic samples one can apply simulation-based methods and if the data are sparse, Monte Carlo simulation or bootstrap technique may be useful.
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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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Understanding the nature of geodetic time series is very important from the point of view of appropriate spectral analysis, filtration and prediction methods application.  
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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.
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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===
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Study of the nature of geodetic time series to choose optimum time series analysis methods  for filtration, spectral analysis, time-frequency analysis  and prediction.
 
  
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Study of the Earth’s rotation and the gravity field variations and their geophysical causes in different frequency bands.
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The objectives of this study group are to:
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* 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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Determination of the significance levels of the results obtained by different time series analysis methods and algorithms applied to geodetic time series.  
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* Study the divergence effect of ultra-high degree spherical and spheroidal harmonic series inside the Brillouin sphere/spheroid.
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* Verify the numerical performance of transformations between spherical and spheroidal harmonic coefficients to ultra-high degree and order.
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Comparison of different time series analysis methods in order to point on their advantages and disadvantages.  
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* Compare least-squares and quadrature approaches to very high-degree and order spherical and spheroidal harmonic analysis.
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* 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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Recommendations of different time series analysis methods for solving problems concerning different geodetic time series.  
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* 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===
  
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Launching of a web page with information concerning time series analysis and it application to geodetic time series with special emphasis on exchange of ideas, providing and updating bibliographic list of references of research results and relevant publications from different disciplines as well as unification of terminology applied in time series analysis.  
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* Providing a platform for increased cooperation between group members, facilitating and encouraging exchange of ideas and research results.
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* 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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Working meetings at the international symposia and presentation of research results at the appropriate sessions.  
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* Organizing working meetings at international symposia and presenting research results in the appropriate sessions.
  
 
===Membership===
 
===Membership===
  
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'' '''Wieslaw Kosek, Poland, chair'''<br /> Michael Schmidt, Germany<br /> Jan Vondrák, Czech Republic<br /> Waldemar Popinski, Poland<br /> Tomasz Niedzielski, Poland<br />Johannes Boehm, Germany<br />Rudolf Widmer-Schnidring, Germany<br />Dawei Zheng, China<br />Yonghong Zhou, China<br />Mahmut O. Karslioglu, Turkey<br />Orhan Akyilmaz, Turkey <br />''
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'' '''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 />''

Latest revision as of 15:33, 24 April 2016

JSG 0.18: 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)

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