Shu, Qingying
(2018)
*Statistical modelling of the near-Earth magnetic field in space weather.*
PhD thesis, University of Glasgow.

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## Abstract

Space weather refers to electromagnetic disturbances in the near-Earth environment as a result of the Sun-Earth interaction. Severe space weather events such as magnetic storms can cause disruption to a wide range of technologies and infrastructure, including communications systems, electronic circuits and power grids. Because of its high potential impact, space weather has been included in the UK National Risk Register since 2011. Space weather monitoring and early magnetic storm detection can be used to mitigate risk in sensitive technological systems. The aim of this project is to investigate the electromagnetic disturbances in the near-Earth environment through developing statistical models that quantifies the variations and uncertainties in the near-Earth magnetic field.

Data of the near-Earth magnetic field arise from in-situ satellite measurements and computer model outputs. The Cluster II mission (Escoubet et al., 2001a) has four satellites that provide in-situ measurements of the near-Earth magnetic field at time-varying locations along their trajectories. The computer model consists of an internal part that calculates the magnetic field sourced from Earth itself and an external part that estimates the magnetic field resulting from the Sun-Earth interaction. These magnetic fields, termed as the internal field and the external field, add up to the total magnetic field. Numerical estimates of the internal field and the external field are obtained respectively from the IGRF-11 model (Finlay et al., 2010) and the Tysganenko-96 (T96) model (Tsyganenko, 2013) given the times and the locations as inputs. The IGRF model outputs are invariant to space weather conditions whereas the T96 model outputs change with the input space weather parameters. The time-varying space weather parameters for T96 model include the solar wind ram pressure, the y and the z-components of the interplanetary magnetic field, and the disturbance storm time index. These parameters are the estimated time series of the solar wind conditions at the magnetopause, i.e. the boundary of the magnetosphere on the day-side, and the disturbance level at the Earth’s surface. Real-time values of the T96 model input parameters are available at hourly resolution from https://omniweb.gsfc.nasa.gov/.

The overall aim of the thesis is to build spatio-temporal models that can be used to understand uncertainties and constraints leveraged from 3D mathematical models of space weather events. These spatio-temporal models can be then used to help understand the design parameters that need to be varied in building a precise and reliable sensor network. Chapter 1 provides an introduction to space weather in terms of the near-Earth magnetic field environment. Beginning with an overview of the near-Earth magnetic field environment, Chapter 2 describes the sources for generating in-situ satellite measurements and computer model outputs, namely the Cluster II mission, the IGRF model, and the T96 model. The process of sampling the magnetic field data from the different data sources and the space-time dependence in the hourly sampled magnetic field data are also included in this Chapter. Converting the space-time structure in the magnetic field data into a time series structure with a function relating the position in space to time, Chapter 3 explores the temporal variations in the sampled in-situ satellite measurements. Through a hierarchical approach, the satellite measurements are related to the computer model outputs. This chapter proposes statistical methods for dealing with the non-stationary features, temporal autocorrelation, and volatility present in the time series data.

With the aim of better characterising the electromagnetic environment around the Earth, Chapter 4 develops time-series models of the near-Earth magnetic field utilising in-situ (CLUSTER) magnetic field data. Regression models linking the CLUSTER satellite observations and two physical models of the magnetic field (T96 and IGRF) are fit to each orbit in the period 2003-2013. The time series of model parameter estimates are then analysed to examine any long term patterns, variations and associations to storm indices. In addition to explaining how the two physical models calibrate with the observed satellite measurements, these statistical models capture the inherent volatility in the magnetic field, and allow us to identify other factors associated with the magnetic field variation, such as the relative position of each satellite relative to the Earth and the Sun. Mixed-effect models that include these factors are constructed for parameters estimated from the regression models for evaluating the performance of the two computer models. Following the calibration of the computer models against the satellite measurements, Chapter 5 investigates how these computer models allow us to investigate the association between the variations in near-Earth magnetic field and storms. To identify the signatures of storm onsets in different locations in the magnetosphere, change-point detection methods are considered for time series magnetic field signals generated from the computer models along various feasible satellite orbits. The detection results inform on potential sampling strategies of the near-Earth magnetic field to be predictive of storms through selecting achievable satellite orbits for placing satellite sensors and detecting changes in the time series magnetic signals.

Chapter 6 provides of a summary of the main finding within this thesis, identifies some limitations of the work carried out in the main chapters, and include a discussion of future research. An Appendix provides details of coordinate transformation for converting the time and position dependent magnetic field data into an appropriate coordinate system.

Item Type: | Thesis (PhD) |
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Qualification Level: | Doctoral |

Keywords: | space weather, near-Earth magnetic field, in-situ satellite measurements, time series, volatility, spatio-temporal model. |

Subjects: | Q Science > QA Mathematics |

Colleges/Schools: | College of Science and Engineering > School of Mathematics and Statistics > Statistics |

Supervisor's Name: | Scott, Prof. Marian, Fletcher, Prof. Lyndsay, Craigmile, Prof. Peter and Ceriotti, Dr. Matteo |

Date of Award: | 2018 |

Depositing User: | Miss Qingying Shu |

Unique ID: | glathesis:2018-8937 |

Copyright: | Copyright of this thesis is held by the author. |

Date Deposited: | 09 Apr 2018 10:08 |

Last Modified: | 26 Apr 2018 10:48 |

URI: | https://theses.gla.ac.uk/id/eprint/8937 |

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