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| − | <big>'''Inverse theory and global optimization'''</big> | + | <big>'''JSG 0.4: Coordinate systems in |
| | + | numerical weather models'''</big> |
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| − | Chair:''C. Kotsakis (Greece)''<br> | + | Chair:''T. Hobiger (Japan)''<br> |
| − | Affiliation:''Comm. 2'' | + | Affiliation:''all Commissions'' |
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| | __TOC__ | | __TOC__ |
| | ===Introduction=== | | ===Introduction=== |
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| − | At the Sapporo IUGG General Assembly (June 30 - July 11, 2003), the International Association of Geodesy (IAG) has approved the establishment of an 'inter-commission' working group (WG) on Inverse Problems and Global Optimization, with the aim of supporting and promoting theoretical and applied research work in various areas of modern geodetic data analysis and inversion. This WG has successfully operated during the last four years under the umbrella of the Intercommission Committee on Theory (ICCT) and the chairmanship of Dr. Juergen Kusche. During the IAG-EC meeting at the Perugia IUGG General Assembly (July 2 - 13, 2007) the new structure of the ICCT and its associated WGs was discussed, and a decision was made that the ICCT/WG on Inverse Problems and Global Optimization will continue its operation for another 4-year period. The purpose of this document is to give an (updated) description of the WG's potential study areas and research objectives, and its associated terms of reference for the upcoming research period 2007 - 2011.
| + | Numerical weather models (NWMs) contain valuable in-formation that is relevant for a variety of geodetic models. Currently no clear description exists regarding how to deal with the NWM coordinate systems when carrying out the calculations in a geodetic reference frame. The problem can be split into two questions: First, how to relate the horizontal NWM coordinates, which are in most cases geocentric coordinates, derived initially from either Carte-sian or spectral representations, properly into an ellipsoi-dal/geodetic frame? Second, how to transform the NWM height system into elliptical heights as used within geo-desy? Although some work has been already done to answer these questions, still no procedures, guidelines or standards have been defined in order to consistently trans-form the meteorological information into a geodetic refer-ence frame. |
| | + | The study group will categorize the NWM coordinate systems, create mathematical models for transformation and summarize these findings in a peer-reviewed paper that will act as guidelines for those who intend to utilize NWM information. In addition, it will be necessary to define such transformations in both ways, in order to enable the assimilation of geodetic measurements into meteorological models as well. Moreover, the study group will deal with the issue of surface data contained in NWM and how this information can be consistently used. |
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| − | ===Terms of Reference=== | + | ===Objectives=== |
| − | | |
| − | It is well recognized that many, if not most, geodetic problems are in fact inverse problems: we know to a certain level of approximation the mathematical and physical models that project an Earth-related parameter space and/or signal onto some data space of finite discrete vectors; given discrete noisy data we then want to recover the governing parameter set or the continuous field (signal) of the underlying model that describes certain geometrical and/or physical characteristics of the Earth. The sitŹuation is further complicated by the fact that these problems are often ill-posed in the sense that only generalized solutions can be retrieved (due to the existence of non-trivial nullspaces) and/or that the solutions do not depend continuously on the given data thus giving rise to dangerous unstable solution algorithms. In order to deal successfully with geodetic data inversion and parameter/signal estimation problems, it is natural that we have to keep track with ongoing developments in inverse problem theory, global optimization theory, multi-parameter regularization techniques, stochastic modeling, Bayesian inversion methods, statistical estimation theory, data assimilation, and other related fields of applied mathematics. In modern geodesy we also have to develop special inversion techniques that can be used for large-scale problems, involving high degree and order gravity field models from space gravity missions and high-resolution discretizations of the density field or the dynamic ocean topography.
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| − | | |
| − | Earth's gravity field modeling from space gravity missions has been (and will surely continue to be in the future) a key study area where existing and newly developed tools from Inverse Problem Theory need to be implemented (including the study of regularization methods and smoothing techniques and the quality assessment of Earth Gravity Models, EGMs). With the cutting-edge applications of the latest and upcoming gravity missions (recovery of monthly surface mass variations from GRACE, constraining viscosity/ lithospheric/postglacial rebound models from GRACE time-variable gravity and from GOCE static geoid pattern analysis), it can be expected that Inverse Problem Theory will increase its importance for the space gravity community.
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| − | | |
| − | Furthermore, there still exist other, more classical geodetic problems that have been identified as inverse and ill-posed and have traditionally attracted the interest of many researchers: the inverse gravitational problem where we are interested in modeling the earth's interior density from gravity observations, various types of downward continuation problems in airborne/satellite gravimetry and geoid determination, certain problems in the context of satellite altimetry and marine gravity modeling, the problem of separating geoid and dynamic ocean topography, the problem of inferring excitations/earth structure parameters from observed polar motion, the determination of stress/strain tensors from observational surface monitoring data, or certain datum definition problems in the realization of global geodetic reference systems. Another, relatively recent, geodetic problem of ill-posed type is the orbit differentiation problem: non-conventional gravity recovery methods like the energy conservation approach and the acceleration approach require GPS-derived kinematic satellite orbits to be differentiated in time, while counteracting noise amplification at the same time. The above nonexhaustive list of inverse problems provides a rich collection of study topics with attractive theoretical/practical aspects, which (in conjunction with the increasing data accuracy, coverage and resolution level) contain several open issues that remain to be resolved.
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| − | ===Objectives===
| + | * Understand the horizontal coordinate systems of the different NWMs, ranging from global to small-scale regional models |
| | + | * Understand the vertical coordinate systems of the differ-ent NWMs, ranging from global to small-scale regional models |
| | + | * Formulate a clear mathematical description on how to transform between NWMs and a geodetic frame (in both directions) |
| | + | * Summarize these findings in a peer-reviewed paper that will act as a standard for future use of NWM-produced fields. |
| | | | |
| − | The aim of the WG is to bring together people working on inverse problem theory and its applications in geodetic problems. Besides a thorough theoretical understanding of inverse problems in geodesy, the WG's central research issue is the extraction of maximum information from noisy data by properly developŹing mathematical/statistical methods in a well defined sense of optimality, and applying them to specific geodetic problems. In particular, the following key objectives are identified:
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| − | * Identification and theoretical understanding of inverse and/or ill-posed problems in modern geodesy
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| − | * Development and comparison of mathematical and statistical methods for the proper treatment of geodetic inverse problems
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| − | * Recommendations and communication of new inversion strategies
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| − | More specific research will focus, for example, on global optimization methods and theory, on the mathematical structure of nullspaces, on the treatment of prior information, on nonlinear inversion in geodetic problems and on the use of techniques for treating inverse problems locally. It is also necessary to investigate the quality assessment and numerical implementation of existing regularization methods in practical geodetic problems (e.g. dealing with coloured noise and/or heterogeneous data, using partially over- and underdetermined models, dealing with different causes of ill-posedness like data gaps and downward continuation, coping with data sets that have entirely unknown noise characteristics, etc.).
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| | | | |
| | ===Program of Activities=== | | ===Program of Activities=== |
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| − | The WG's activities will include the launching of a webpage for dissemination of information, for presentation, communication and monitoring of research results and related activities, and for providing an updated bibliographic list of references for relevant papers and reports in the general area of geodetic inverse problems. This would also provide WG's members (and other interested individuals) with a common platform to communicate individual views and results, and stimulate discussions. Although the discussion will be in general based on email, it is planned to have splinter meetings during international conferences and, if possible, a workshop or a special conference session.
| + | Launch a web-page for dissemination of information, pre-sentation, communication, outreach purposes; provide a bibliography |
| − | | + | Conduct working meetings in association with inter-national conferences; present research results in appropri-ate sessions |
| − | ===Membership===
| + | Organize workshops dedicated mainly to problem identifi-cation and to motivation of relevant scientific research |
| | + | Produce at least one peer-reviewed paper that presents a clear and consistent description of how to transform in-formation from and to NWMs, and the relevance of different NWM structures, and, if possible, a second paper that deals with the uncertainty of the NWM related coordinate information will be considered. |
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| − | The following is a proposed (tentative) membership list for the IAG/ICCT WG on Inverse Problems and Global Optimization. The final list will be confirmed within 2007.
| + | ===Members=== |
| | | | |
| − | '' '''C. Kotsakis (Greece, chair)'''<br /> J. Kusche (Germany)<br /> S. Baselga Moreno (Spain)<br /> J. Bouman (The Netherlands)<br /> P. Ditmar (The Netherlands)<br /> B. Gundlich (Germany)<br /> P. Holota (Czech Republic)<br /> M. Kern (The Netherlands)<br /> T. Mayer-Guerr (Germany)<br /> V. Michel (Germany)<br /> P. Novák (Czech Republic)<br /> S. Pereverzev (Austria)<br /> B. Schaffrin (USA)<br /> M. Schmidt (Germany)<br /> Y. Shen (China)<br /> N. Sneeuw (Germany)<br /> S. Tikhotsky (Germany)<br /> C. Xu (Russia)<br />'' | + | '' '''Thomas Hobiger (Japan), chair'''<br />Johannes Boehm (Austria)<br /> |
| | + | Tonie van Dam (Luxembourg)<br />Pascal Gegout (France)<br />Rüdiger Haas (Sweden)<br />Ryuichi Ichikawa (Japan)<br /> |
| | + | Arthur Niell (USA)<br />Felipe Nievinski (USA)<br />David Salstein (USA)<br />Marcelo Santos (Canada)<br />Michael Schindelegger (Austria)<br />Henrik Vedel (Denmark)<br />Jens Wickert (Germany)<br />Florian Zus (Germany)<br />'' |
JSG 0.4: Coordinate systems in
numerical weather models
Chair:T. Hobiger (Japan)
Affiliation:all Commissions
Introduction
Numerical weather models (NWMs) contain valuable in-formation that is relevant for a variety of geodetic models. Currently no clear description exists regarding how to deal with the NWM coordinate systems when carrying out the calculations in a geodetic reference frame. The problem can be split into two questions: First, how to relate the horizontal NWM coordinates, which are in most cases geocentric coordinates, derived initially from either Carte-sian or spectral representations, properly into an ellipsoi-dal/geodetic frame? Second, how to transform the NWM height system into elliptical heights as used within geo-desy? Although some work has been already done to answer these questions, still no procedures, guidelines or standards have been defined in order to consistently trans-form the meteorological information into a geodetic refer-ence frame.
The study group will categorize the NWM coordinate systems, create mathematical models for transformation and summarize these findings in a peer-reviewed paper that will act as guidelines for those who intend to utilize NWM information. In addition, it will be necessary to define such transformations in both ways, in order to enable the assimilation of geodetic measurements into meteorological models as well. Moreover, the study group will deal with the issue of surface data contained in NWM and how this information can be consistently used.
Objectives
- Understand the horizontal coordinate systems of the different NWMs, ranging from global to small-scale regional models
- Understand the vertical coordinate systems of the differ-ent NWMs, ranging from global to small-scale regional models
- Formulate a clear mathematical description on how to transform between NWMs and a geodetic frame (in both directions)
- Summarize these findings in a peer-reviewed paper that will act as a standard for future use of NWM-produced fields.
Program of Activities
Launch a web-page for dissemination of information, pre-sentation, communication, outreach purposes; provide a bibliography
Conduct working meetings in association with inter-national conferences; present research results in appropri-ate sessions
Organize workshops dedicated mainly to problem identifi-cation and to motivation of relevant scientific research
Produce at least one peer-reviewed paper that presents a clear and consistent description of how to transform in-formation from and to NWMs, and the relevance of different NWM structures, and, if possible, a second paper that deals with the uncertainty of the NWM related coordinate information will be considered.
Members
Thomas Hobiger (Japan), chair
Johannes Boehm (Austria)
Tonie van Dam (Luxembourg)
Pascal Gegout (France)
Rüdiger Haas (Sweden)
Ryuichi Ichikawa (Japan)
Arthur Niell (USA)
Felipe Nievinski (USA)
David Salstein (USA)
Marcelo Santos (Canada)
Michael Schindelegger (Austria)
Henrik Vedel (Denmark)
Jens Wickert (Germany)
Florian Zus (Germany)
