Difference between pages "IC SG7" and "IC SG9"

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<big>'''JSG 0.7: Computational methods for high-resolution gravity field modelling and nonlinear dif-fusion filtering'''</big>
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<big>'''Application of time-series analysis in geodesy'''</big>
  
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Chairs: ''R. Čunderlík (Slovakia), K. Mikula (Slovakia)''<br>
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Chair: ''W. Kosek (Poland)''<br>
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Affiliation: ''Comm. 2, 3 and GGOS''
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Affiliation:''Comm. 1, 2, 3, 4''
  
 
__TOC__
 
__TOC__
 
===Introduction===
 
===Introduction===
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Efficient numerical methods and HPC (High Performance Computing) facilities provide new opportunities in many applications in geodesy. The goal of the IC SG is to apply numerical methods like the finite element method (FEM), finite volume method (FVM), boundary element method (BEM) and others mostly for gravity field modelling and non-linear filtering of data on the Earth’s surface. An advantage is that such numerical methods use finite elements as basis functions with local supports. Therefore a refinement of the discretization is very straightforward allowing adaptive refinement procedures as well.
 
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In case of gravity field modelling, a parallelization of algorithms using the standard MPI (Message Passing Interface) procedures and computations on clusters with distributed memory allows to achieve global or local gravity field models of very high-resolution, where a level of the discretization practically depends on capacity of available HPC facilities. The aforementioned numerical methods allow a detailed discretization of the real Earth’s surface considering its topography. To get precise numerical solution to the geodetic boundary-value problems (BVPs) on such complicated surface it is also necessary handle problems like the oblique derivative.
 
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Data filtering occurs in many applications of geosciences. A quality of filtering is essential for correct interpretations of obtained results. In geodesy we usually use methods based on the Gaussian filtering that corresponds to a linear diffusion. Such filtering has a uniform smoothing effect, which also blurs “edges” representing important structures in the filtered data. In contrary, a nonlinear diffusion allows adaptive smoothing that can preserve main structures in data, while a noise is effectively reduced. In image processing there are known at least two basic nonlinear diffusion models; (i) the regularized Perona-Malik model, where the diffusion coefficient depends on an edge detector, and (ii) the geodesic mean curvature flow model based on a geometrical diffusion of level-sets of the image intensity.
 
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The aim of the SG is to investigate and develop nonlinear filtering methods that would be useful for a variety of geodetic data, e.g., from satellite missions, satellite altimetry and others. A choice of an appropriate numerical technique is open to members of the SG. An example of the proposed approach is based on a numerical solution of partial differential equations using a surface finite volume method. It leads to a semi-implicit numerical scheme of the nonlinear diffusion equation on a closed surface.
 
  
 +
Observations of the new space geodetic techniques (geometric and gravimetric) deliver a global picture of dynamics of the Earth usually represented in the form of  time series which describe 1) changes of the surface geometry of the Earth due to horizontal and vertical deformations of the land surface, variations of 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 as well as the variations of the centre of mass of the Earth. Geometry, Earth rotation and the gravity field are the three components of the Global Geodetic Observing System (GGOS). The vision of GGOS is to integrate all observations and elements of the Earth’s system into one unique physical and mathematical model. However, 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.
 +
 +
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. The techniques of time frequency spectrum and coherence may be developed further to display reliably the features of the temporal or spatial variability of signals existing in various geodetic data, as well as in other data sources.
 +
 +
Geodetic time series may include for example variations of site positions, tropospheric delay, ionospheric total 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 the 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 the application of digital filters for extracting specific components with a chosen frequency bandwidth. 
 +
 +
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 the raw data. The topic on the improvement of the edge effects in time series analysis may also be 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.
 +
 +
Understanding the nature of geodetic time series is very important from the point of view of appropriate spectral analysis as well as application of filtering and prediction methods.
 +
 +
__TOC__
 
===Objectives===
 
===Objectives===
  
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* to develop numerical models for solving the geodetic BVPs using numerical methods like FEM, FVM, BEM and others,
+
Study of the nature of geodetic time series to choose optimum time series analysis methods for filtering, spectral analysis, time frequency analysis and prediction.
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* to investigate the problem of oblique derivative,
+
 
−
* to implement parallelization of numerical algorithms using the standard MPI procedures,
+
Study of Earth rotation and gravity field variations and their geophysical causes in different frequency bands. 
−
* to perform large-scale parallel computations on clusters with distributed memory,
+
 
−
* to investigate methods for nonlinear filtering of data on closed surfaces using the regularized Perona-Malik model or mean curvature flow model,
+
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.
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* to derive fully-implicit and semi-implicit numerical schemes for the linear and nonlinear diffusion equation on closed surfaces using the surface FVM,
+
 
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* to develop algorithms for the nonlinear filtering of data on the Earth’s surface,
+
Determination of the statistical significance levels of the results obtained by different time series analysis methods and algorithms applied to geodetic time series.
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* to summarize the developed methods and achieved numerical results in journal papers.
+
 
 +
Comparison of different time series analysis methods in order to point out their advantages and disadvantages.
 +
 
 +
Recommendations of different time series analysis methods for solving problems concerning specific geodetic time series.
  
 
===Program of activities===
 
===Program of activities===
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active participation in major geodetic conferences,
 
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working meetings at international symposia,
 
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organization of a conference session.
 
  
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===Members===
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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.
 +
 
 +
Working meetings at the international symposia and presentation of research results at the appropriate sessions.
 +
 
 +
===Membership===
  
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'' '''Róbert Čunderlík (Slovakia), chair<br />
+
'' '''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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Karol Mikula (Slovakia), chair'''<br />
 
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Ahmed Abdalla, New Zealand<br />
 
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Michal Beneš (Czech Republic)<br />
 
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Zuzana Fašková (Slovakia)<br />
 
−
Marek Macák (Slovakia)<br />
 
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Otakar Nesvadba (Czech Republic)<br />
 
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Róbert Špir (Slovakia)<br />
 
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Róbert Tenzer (New Zealand)<br />''
 

Revision as of 19:21, 18 July 2008

Application of time-series analysis in geodesy

Chair: W. Kosek (Poland)
Affiliation:Comm. 1, 2, 3, 4

Introduction

Observations of the new space geodetic techniques (geometric and gravimetric) deliver a global picture of dynamics of the Earth usually represented in the form of time series which describe 1) changes of the surface geometry of the Earth due to horizontal and vertical deformations of the land surface, variations of 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 as well as the variations of the centre of mass of the Earth. Geometry, Earth rotation and the gravity field are the three components of the Global Geodetic Observing System (GGOS). The vision of GGOS is to integrate all observations and elements of the Earth’s system into one unique physical and mathematical model. However, 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.

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. The techniques of time frequency spectrum and coherence may be developed further to display reliably the features of the temporal or spatial variability of signals existing in various geodetic data, as well as in other data sources.

Geodetic time series may include for example variations of site positions, tropospheric delay, ionospheric total 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 the 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 the application of digital filters for extracting specific components with a chosen frequency bandwidth.

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 the raw data. The topic on the improvement of the edge effects in time series analysis may also be 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.

Understanding the nature of geodetic time series is very important from the point of view of appropriate spectral analysis as well as application of filtering and prediction methods.


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 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.

Recommendations of different time series analysis methods for solving problems concerning specific geodetic time series.

Program of activities

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.

Working meetings at the international symposia and presentation of research results at the appropriate sessions.

Membership

Wieslaw Kosek, Poland, chair
Michael Schmidt, Germany
Jan Vondrák, Czech Republic
Waldemar Popinski, Poland
Tomasz Niedzielski, Poland
Johannes Boehm, Germany
Rudolf Widmer-Schnidring, Germany
Dawei Zheng, China
Yonghong Zhou, China
Mahmut O. Karslioglu, Turkey
Orhan Akyilmaz, Turkey

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