Difference between revisions of "JSG T.33"

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<big>'''JSG 0.20: High resolution harmonic analysis and synthesis of potential fields'''</big>
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<big>'''JSG T.33: Time series in geodesy and geodynamics'''</big>
  
Chair: ''Sten Claessens (Australia)''<br>
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Chair: '': Wieslaw Kosek (Poland)''<br>
Affiliation:''Comm. 2 and GGOS''
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Affiliation:''Commissions 1, 3 and 4, GGOS''
  
 
__TOC__
 
__TOC__
  
===Terms of Reference===
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===Introduction===
  
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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Observations of the space geodesy techniques enable measuring Earth’s gravity variations caused by mass displacement, the change in the Earth’s shape, and the change in the Earth’s rotation. The Earth’s rotation represented by the Earth Orientation Parameters (EOP) should be observed with possibly the smallest latency to provide real-time transformation between the International Terrestrial and Celestial Reference Frames (ITRF and ICRF). Observed by GRACE missions, redistribution of mass within the fluid layers relative to the solid Earth induces exchange of angular momentum between these layers and solid Earth, changes in the Earth’s inertia tensor.
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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Redistribution of masses induce temporal variations of Earth's gravity field where 1 degree spherical harmonics correspond to the Earth’s centre of mass variations (long term mean of them determines the ITRF origin) and 2 degree spherical harmonics correspond to Earth rotation changes.  Satellite altimetry enables observation of changes in geometry of sea level and space geodesy techniques enable observations of changes in geometry of the Earth's crust by monitoring horizontal and vertical deformations of site positions. Sea surface height varies due to thermal expansion of sea water and changes in ocean water mass arising from melting polar ice cap, mountain glacier ice, as well as due to groundwater storage. The site positions which are determined together with satellite orbit parameters (in the case of SLR, GNSS and DORIS) or radio source coordinates (in the case of VLBI) and Earth orientation parameters (x, y pole coordinates, UT1-UTC/LOD and precession-nutation corrections dX, dY) are then used to build the global ITRF which changes due to e.g. plate tectonics, postglacial rebound, atmospheric, hydrology and ocean loading and earthquakes. In these three components of geodesy which should be integrated into one unique physical and mathematical model there are changes that are described by spatial and temporal geodetic time series.  
  
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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Different time series analysis methods have been applied to analyze all elements of the Earth’s system for better understanding the mutual relationship between them. The nature of considered signals in the geodetic time series is mostly wideband, irregular and non-stationary. Thus, it is recommended to apply spectra-temporal analyzes methods to analyze and compare these series to explain the mutual interaction between them in different time and different frequency bands. The main problems to deal with is to estimate the deterministic (including trend and periodic variations) and stochastic (non-periodic variations and random changes described by different noise characters) components in these geodetic time series as well as to apply the appropriate methods of spectra-temporal comparison of these series.  
 +
The multiple methods of time series analysis may be encouraged to be applied to the preprocessing of raw data from various geodetic measurements in order to promote the quality level of enhancement of signals existing in these data. The topic on the improvement of the edge effects in time series analysis should be also considered, since they may affect the reliability of long-range tendency (trends) estimated from data series as well as the real-time data processing and prediction. 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.  
  
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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Measurements by space geodetic techniques provide an important contribution to the understanding of climate change. The analysis of Earth rotation and geophysical time series as well as global sea level variations shows that there is a mutual relationship between them for oscillations with periods from a few days to decades. The thermal annual cycle caused by the Earth's orbital motion modified by variable solar activity induces seasonal variations the Earth’s fluid layers, thus in the Earth rotation, sea level variations as well as in the changes of the Earth's gravity field and centre of mass. The interrelationships between the geodetic time series and changes of global troposphere temperature show that they provide very important information about the Earth's climate change (for example global sea level increases faster during El Nino events associated with the increase of global temperature and in this time the increase of length of day can be also noticed). Thus, the spectra-temporal analysis and comparison of geodetic time series should also include time series associated with solar activity.    
 
 
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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* Study of the nature of geodetic time series to choose optimum time series analysis methods for filtering, spectral analysis, time frequency analysis and prediction.
* 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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* Study of Earth's geometry, rotation and gravity field variations and their geophysical causes in different frequency bands.
* Study the divergence effect of ultra-high degree spherical and spheroidal harmonic series inside the Brillouin sphere/spheroid.
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* Evaluation of appropriate covariance matrices for the time series by applying the law of error propagation to the original measurements, including weighting schemes, regularization, etc.
* Verify the numerical performance of transformations between spherical and spheroidal harmonic coefficients to ultra-high degree and order.
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* Determination of the statistical significance levels of the results obtained by different time series analysis methods and algorithms applied to geodetic time series.
* Compare least-squares and quadrature approaches to very high-degree and order spherical and spheroidal harmonic analysis.
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* Comparison of different time series analysis methods in order to point out their advantages and disadvantages.
* 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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* Application and development of time frequency analysis methods to detect the relationship between geodetic time series and time series associated with the solar activity in order to solve the problems related to the climate change.  
* 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.
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* Recommendations of different time series analysis methods for solving problems concerning specific geodetic time series.
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* Detection of reliable station velocities and their uncertainties with taking into account their non-linear motion and environmental loadings and identification of site clusters with similar velocities
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* Deterministic and stochastic modelling and prediction of troposphere and ionosphere parameters for real time precise GNSS positioning.  
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* Better Earth Orientation Parameters short-term prediction using the extrapolation models of the fluid excitation functions.
  
 
===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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* Organization of a session on time series analysis in geodesy at the Hotine-Marussi Symposium in 2022.
* 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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* Co-organization of the PICO sessions "Mathematical methods for the analysis of potential field data and geodetic time series" at the European Geosciences Union General Assemblies in Vienna, Austria.
* Organizing working meetings at international symposia and presenting research results in the appropriate sessions.
 
  
 
===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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'' '''Wieslaw Kosek (Poland), chair ''' <br /> Orhan Akyilmaz (Turkey) <br /> Johannes Boehm (Austria) <br /> Xavier Collilieux (France) <br /> Olivier de Viron (France) <br /> Laura Fernandez (Argentina) <br /> Richard Gross (USA) <br /> Mahmut O. Karslioglu (Turkey) <br /> Anna Kłos (Poland) <br /> Hans Neuner (Germany) <br /> Tomasz Niedzielski (Poland) <br /> Sergei Petrov (Russia) <br /> Waldemar Popiński (Poland) <br /> Michael Schmidt (Germany) <br /> Michel Van Camp (Belgium) <br /> Jan Vondrák (Czech Republic) <br /> Dawei Zheng (China) <br /> Yonghong Zhou (China) <br />''

Latest revision as of 11:48, 10 June 2020

JSG T.33: Time series in geodesy and geodynamics

Chair: : Wieslaw Kosek (Poland)
Affiliation:Commissions 1, 3 and 4, GGOS

Introduction

Observations of the space geodesy techniques enable measuring Earth’s gravity variations caused by mass displacement, the change in the Earth’s shape, and the change in the Earth’s rotation. The Earth’s rotation represented by the Earth Orientation Parameters (EOP) should be observed with possibly the smallest latency to provide real-time transformation between the International Terrestrial and Celestial Reference Frames (ITRF and ICRF). Observed by GRACE missions, redistribution of mass within the fluid layers relative to the solid Earth induces exchange of angular momentum between these layers and solid Earth, changes in the Earth’s inertia tensor.

Redistribution of masses induce temporal variations of Earth's gravity field where 1 degree spherical harmonics correspond to the Earth’s centre of mass variations (long term mean of them determines the ITRF origin) and 2 degree spherical harmonics correspond to Earth rotation changes. Satellite altimetry enables observation of changes in geometry of sea level and space geodesy techniques enable observations of changes in geometry of the Earth's crust by monitoring horizontal and vertical deformations of site positions. Sea surface height varies due to thermal expansion of sea water and changes in ocean water mass arising from melting polar ice cap, mountain glacier ice, as well as due to groundwater storage. The site positions which are determined together with satellite orbit parameters (in the case of SLR, GNSS and DORIS) or radio source coordinates (in the case of VLBI) and Earth orientation parameters (x, y pole coordinates, UT1-UTC/LOD and precession-nutation corrections dX, dY) are then used to build the global ITRF which changes due to e.g. plate tectonics, postglacial rebound, atmospheric, hydrology and ocean loading and earthquakes. In these three components of geodesy which should be integrated into one unique physical and mathematical model there are changes that are described by spatial and temporal geodetic time series.

Different time series analysis methods have been applied to analyze all elements of the Earth’s system for better understanding the mutual relationship between them. The nature of considered signals in the geodetic time series is mostly wideband, irregular and non-stationary. Thus, it is recommended to apply spectra-temporal analyzes methods to analyze and compare these series to explain the mutual interaction between them in different time and different frequency bands. The main problems to deal with is to estimate the deterministic (including trend and periodic variations) and stochastic (non-periodic variations and random changes described by different noise characters) components in these geodetic time series as well as to apply the appropriate methods of spectra-temporal comparison of these series. The multiple methods of time series analysis may be encouraged to be applied to the preprocessing of raw data from various geodetic measurements in order to promote the quality level of enhancement of signals existing in these data. The topic on the improvement of the edge effects in time series analysis should be also considered, since they may affect the reliability of long-range tendency (trends) estimated from data series as well as the real-time data processing and prediction. 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.

Measurements by space geodetic techniques provide an important contribution to the understanding of climate change. The analysis of Earth rotation and geophysical time series as well as global sea level variations shows that there is a mutual relationship between them for oscillations with periods from a few days to decades. The thermal annual cycle caused by the Earth's orbital motion modified by variable solar activity induces seasonal variations the Earth’s fluid layers, thus in the Earth rotation, sea level variations as well as in the changes of the Earth's gravity field and centre of mass. The interrelationships between the geodetic time series and changes of global troposphere temperature show that they provide very important information about the Earth's climate change (for example global sea level increases faster during El Nino events associated with the increase of global temperature and in this time the increase of length of day can be also noticed). Thus, the spectra-temporal analysis and comparison of geodetic time series should also include time series associated with solar activity.

Objectives

  • Study of the nature of geodetic time series to choose optimum time series analysis methods for filtering, spectral analysis, time frequency analysis and prediction.
  • Study of Earth's geometry, rotation and gravity field variations and their geophysical causes in different frequency bands.
  • Evaluation of appropriate covariance matrices for the time series by applying the law of error propagation to the original measurements, including weighting schemes, regularization, etc.
  • Determination of the statistical significance levels of the results obtained by different time series analysis methods and algorithms applied to geodetic time series.
  • Comparison of different time series analysis methods in order to point out their advantages and disadvantages.
  • Application and development of time frequency analysis methods to detect the relationship between geodetic time series and time series associated with the solar activity in order to solve the problems related to the climate change.
  • Recommendations of different time series analysis methods for solving problems concerning specific geodetic time series.
  • Detection of reliable station velocities and their uncertainties with taking into account their non-linear motion and environmental loadings and identification of site clusters with similar velocities
  • Deterministic and stochastic modelling and prediction of troposphere and ionosphere parameters for real time precise GNSS positioning.
  • Better Earth Orientation Parameters short-term prediction using the extrapolation models of the fluid excitation functions.

Program of activities

  • Organization of a session on time series analysis in geodesy at the Hotine-Marussi Symposium in 2022.
  • Co-organization of the PICO sessions "Mathematical methods for the analysis of potential field data and geodetic time series" at the European Geosciences Union General Assemblies in Vienna, Austria.

Membership

Wieslaw Kosek (Poland), chair
Orhan Akyilmaz (Turkey)
Johannes Boehm (Austria)
Xavier Collilieux (France)
Olivier de Viron (France)
Laura Fernandez (Argentina)
Richard Gross (USA)
Mahmut O. Karslioglu (Turkey)
Anna Kłos (Poland)
Hans Neuner (Germany)
Tomasz Niedzielski (Poland)
Sergei Petrov (Russia)
Waldemar Popiński (Poland)
Michael Schmidt (Germany)
Michel Van Camp (Belgium)
Jan Vondrák (Czech Republic)
Dawei Zheng (China)
Yonghong Zhou (China)