Evolution of Large Scale Current Systems
Satellites in various orbits in the magnetosphere make direct measurements of physical quantities. For intermittent physical processes (i.e. substorms) they must be in the right place at the right time. This does not happenfrequently since the magnetosphere is quite large. In addition, there is a
occur before an event is of particular importance. Therefore, while space based measurements are important they are limited by their sparsity in space and their ability to measure continuously in one spatial location over extended periods of time (barring geostationary satellites in the inner magnetosphere). To supplement space based measurements a continual monitoring of the large scale systm would be invaluable. Ground based measurements are cur- rently the only reasonable way to accomplish this. Magnetometer and radar measurements are the primary ground based measurements. Radar measure- ments use the Doppler effect to measure the line of sight bulk flow velocity of ions in the E and F regions of the ionosphere. By assuming the flow of ions is from the E ×B drift, the electric potential in the ionosphere can be determined (see figure 1.18). Hence, to fully reconstruct the convection system there needs to be multiple radars looking at the same parcel of plasma from dif- ferent angles. Alternatively, time separated measurements could be used. The radars move through magnetic local time (Magnetic Local Time (MLT)). MLT is defined by the position of the Earth-Sun line as such geographic positions move through MLT. By considering two time separated radar measurements the same reconstruction can be achieved albeit under the big assumption that the system has not changed significantly during that period of time.
Magnetometers measure perturbations in the magnetic field, usually af- ter being baselined (i.e. removal of Earth’s background field and other see chapter 2.1). The magnetic perturbations result from ionospheric current sys- tems. The ionosphere is coupled to the rest of the magnetosphere via magnetic field lines that thread through both systems. Hence, these currents are a proxy for physical processes that are occurring in the magnetosphere.
sphere has increase remarkably over the past∼70 years, however, useful ways of quantifying the global response has been lacking. Historically magnetometer time series were individually inspected during major geomagnetic disturbances or large scale scalar indices such as the auroral indices (AE, AU and AL) and DST were used (see section 1.5.1). The former is time consuming considering the large quantities of data now available and the latter is incredibly limiting as it provides no spatial information.
One goal is to completely reconstruct the global ionospheric current system from magnetic measurements. Under the assumption that the mag- netic field perturbations result predominantly from Hall currents, equivalent currents can be reconstructed. In this method the ionospheric conductivities are also assumed. This is problematic during highly disturbed periods where strong FAC cause additional ionisation. The method is improved with the introduction of supplementary measurements and models for the conductivity. This falls under the umbrella of the assimilative mapping of ionospheric elec- trodynamics (Assimilative Mapping of Ionospheric Electrodynamics (AMIE)) technique Richmond [1992]. While an improvement, some assumptions about conductivity and the weighting to the different measurement is still present within the technique.
A difficulty presented all techniques related to the mapping of the spatio-temporal evolution of the ionosphere currents is the large gaps in cover- age. One solution to this is to interpolate the data to fill in gaps in the coverage, this has been done with radar measurements [Ruohoniemi and Baker, 1998] and more recently ground station measurements [Waters et al., 2015]. Both methods involve fitting the data to a set of spherical harmonic functions, hence the general shape of the solution is restricted and is not unique. Alternatively,
a statistical approach can be taken in which the gaps in the data coverage are filled in by aggregating over many similar events [Gjerloev and Hoffman, 2014]. This approach has problems since there is likely significant time and spatial smearing due to the different global responses during the individual events.
Dynamical networks may be a potential method for mapping the spatio- temporal evolution of the system. Dynamical networks can be constructed by quantifying the similarity between measurements at different spatial locations as a function of time. This would give a measure of how coherent the system (or components of the system) responds to external (direct driving of magne- tosphere by solar wind) and internal (substorms) forcing of the system. In a simplified view, the spatial pattern of connections would be indicative of the locations of the large scale ionospheric currents. This framework has obvious benefits over current established measures of geomagnetic activity such as AE and DST, which do not contain any spatial information. In addition, other methods for quantifying the current systems have to make assumptions about the system such as the conductivity. Ultimately dynamical network provide a unique unexplored interpretation of the ionospheric/magnetospheric system. Only ground measurements are required for the analysis, as such, large quan- tities of historic data can be leveraged to achieve a wide breadth of scientific aims.
The structure of the thesis is as follows. In chapter 2 we describe our methods for determining the networks, what we use as nodes, what methods we use to determine connections between nodes, how we use the similarity thresholds to account for inherent difference between nodes and how we map the network information onto a regular grid. In chapter 3 we construct net-
works for 4 test case substorms and define network parameters that describe the spatial distribution of similarity. In chapter 4 we construct the statistical response of the gridded network to north-south and south north IMF turnings. In chapter 5 we give our conclusions and potential future work.