Rigorous computation of high resolution spherical harmonic gravity models on massive parallel computer systems
Final Report Abstract
Due to the use of autonomous sensors to collect geodetic data sets, the data sets to be analyzed get more and more complex and the computational requirements to derive an in a computational sense rigorous solution, significantly increase. Especially sensors observing the global System Earth - e.g. carried on satellite platforms - deliver huge data sets, as they either have a high measurement frequency, deliver observation time series over decades or even both. Thus refined higher resolution models, either in space and/or in time, can be adjusted to the measurements resulting in a higher dimensional parameter space of the models. This often results in an inverse model and an overdetermined system of equations has to be solved with respect to the unknown model parameters. In addition to the increasing number of observations (hundreds of thousands to hundreds of millions) and the increasing number of unknown model parameters (tens of thousands to millions) the observations are often highly correlated and require a complex stochastic model for a proper use within a least squares adjustment with complementary observation types. Within this project, concepts, methods and standards from high performance computing were used to develop and implement, in a numerical sense, rigorous solvers for high and huge dimensional least squares adjustment problems. Representative problems from global gravity field determination (spherical harmonic analysis) were chosen to demonstrate the use of this high performance computing concepts for the analysis of typical geodetic data sets. Within this project a massive parallel software package for high dimensional adjustment problems (with special focus on spherical harmonic analysis) was developed to make problems solvable, which were not rigorously computable before. Besides the general framework and the basic functionality for adjustment procedures, specific and optimized modules were developed for applications from gravity field determination. It was shown in detail, how this special extension can be implemented using the developed basic framework. The design was kept flexible to easily introduce/adapt alternative observation types or adjustment procedures. The main parts of the solver can be used on only a small compute core grid (e.g. with only 2 cores) or on huge compute core grids which make use of ten thousands of compute cores. In addition, a specific adaption to any other geodetic application, which requires the solution of high dimensional adjustment problem is possible and the software was prepared for that. This project demonstrates the value of high performance computing concepts for geodetic applications. Historical established approximations and simplifications, which are still widely used in many studies, often become decrepit, using the concepts of high performance computing. Avoiding approximations and simplifications has a positive effect for the solution itself as well as for the corresponding error estimate in form of the covariance matrix, although the positive effect can not be quantified. The basics towards an extension of the OEQs was made (increased parameter space), such that many tasks can be solved in a joint adjustment. Thus multi step approaches can be replaced by a joint inversion. Although a lot of effort has to be spent on the fusion of high performance computing concepts with established algorithms and the knowledge of the data handling, the project demonstrates that, if the basics are implemented and understood, their use is straightforward.
Publications
- A concept for the estimation of high-degree gravity field models in a high performance computing environment. Studia Geophysica et Geodaetica, 58:571–594, 2014
J. M. Brockmann, L. Roese-Koerner, and W.-D. Schuh
(See online at https://doi.org/10.1007/s11200-013-1246-3) - Mean dynamic topography estimates purely based on GOCE gravity field models and altimetry. Geophysical Research Letters, 41(6):2063–2069, 2014
S. Becker, J. M. Brockmann, and W.-D. Schuh
(See online at https://doi.org/10.1002/2014GL059510) - On High Performance Computing in Geodesy – Applications in Global Gravity Field Determination. PhD thesis, Institute of Geodesy and Geoinformation, University of Bonn, Bonn, Germany, 2014
J. M. Brockmann
- Use of high performance computing for the rigorous estimation of very high degree spherical harmonic gravity field models. In U. Marti, editor, Procceedings of the International Symposium on Gravity, Geoid and Height Systems (GGHS2012), p. 27–33. Springer Berlin Heidelberg, 2015
J. M. Brockmann, L. Roese-Koerner, and W.-D. Schuh
(See online at https://doi.org/10.1007/978-3-319-10837-7_4) - Computational aspects of high-resolution global gravity field u determination - numbering schemes and reordering. In K. Binder, M. Müller, M. Kremer, and A. Schnurpfeil, editors, NIC Symposium 2016, volume 48 of NIC Series, Jülich, Germany
J. M. Brockmann and W.-D. Schuh
