Knowledge of the solar corona's 3D distribution of density and temperature is needed to model the propagation of solar disturbances from the Sun's surface out to the near-Earth environment, where effects on space-weather may be observed, experienced and, ultimately, mitigated. Current and next generation Sun observing spacecraft are providing us with unprecedented access to, and challenging amounts of, data regarding the three dimensional and time varying structure of the corona.
Dynamic solar rotational tomography (SRT) is the approach that this collaboration of geoscientists and statisticians from the University of Illinois (Urbana-Champaign) will develop under a NSF interdisciplinary program, Collaborations in Mathematical Geosciences. Their approach seeks the development of Monte Carlo filtering algorithms optimized for non-linear and non-Gaussian probability distribution functions. To be capable of handling the large data sets associated with these tomographic problems requires progress in statistical estimation theory as well as the design of efficient computational algorithms.
As well as benefiting the broader geophysical and statistical communities, graduate and undergraduate research and training to take between the two disciplinary areas provides an important educational incentive for the work. Tomographic particle filtering techniques, such as those proposed here, may have additional applications of interest to other fields in the geosciences, as well as in engineering and biomedical imaging.
The current generation of Sun-observing spacecraft give the scientific community an unprecedented amount of information about the three-dimensional (3D) structure of the Sun’s corona, and Bayesian tomographic analysis of these data have the potential to address a number of longstanding issues in space weather and solar plasma physics. In particular, solar rotational tomography (SRT) allows one to use time series of whitelight and extreme ultraviolet (EUV) images to make empirical determinations of the global, 3D distribution of density and temperature in the Sun’s corona. This information is critical for addressing the long standing theoretical problems of identifying the processes that heat the corona’s plasma and drive the solar wind. Knowledge of the corona’s 3D structure is also needed to model the propagation of solar disturbances out to the near-Earth space environment so that the adverse effects of space weather can be understood and ultimately mitigated. This research is timed to take advantage of the historic scientific opportunity provided by simultaneous data from 3 widely separated NASA spacecraft. The goal of this project is to develop efficient Monte Carlo filtering algorithms for handling such large data sets and apply them to multi-spacecraft data sets. We developed the localized ensemble Kalman filter (EnKF) for large-scale dynamic tomography problems. The algorithm makes use of new spatial localization concepts to dramatically reduce computational complexity and enable time-dependent tomographic imaging of dynamic objects such as the solar corona. We applied the new EnKF on a data from the ground-based Mk4 coronagraph at the Mauna Loa Solar Observatory, the space-based C2 coronagraph onboard the SOHO spacecraft, and the space-based COR1 coronagraphs onboard the dual STEREO spacecraft. We also developed a new particle filter algorithm for online filtering problems in nonlinear state space models. The methods we developed will be quite relevant to dynamic tomography problems encountered in other fields as well (e.g., X-ray tomographic reconstruction of the beating heart). A series of papers were published or submitted for publication. The project funds provide support for several graduate students from the Department of Electrical and Computer Engineering, Department of Statistics, and Department of Computer Science. All of the graduate assistants have gained experience with numerical analysis, computer programming and scientific writing. The research has been incorporated into graduate and undergraduate courses. The project members have presented results of research under this grant at many conferences and departmental seminars.
