The “Average” Substorm

In this section we provide a cursory look at the aggregate network response to substorms. In chapter 1.5.1 we describe a few features that are usually present during a substorm, the localised onset brightening of the aurora oval, a rapid intensification of the westward electrojet (a rapid decrease in AL), dipolarisa- tion of magnetic field in the near tail region and bulk Earthward flows. Several of these features are usually only visible from space, where measurements are not continuous, hence, there is sometimes uncertainty on whether a substorm is occurring. A way of identifying substorms from ground measurements only would be invaluable. The first step in doing so is to construct an aggregate network response for substorms.

In the same manner as outlined in section 3.1 we identify 116 isolated substorms and their onset times. We obtain networks for these events in an identical manner to the test case substorms following the methods outlined in chapter 2. In order to obtain the average response network to isolated substorms we first map the individual networks onto a regular grid by the methods outlined in chapter 2.5. A∗_kl(q)(τ) and A∗∗_kl(q)(τ) now represent the

gridded network response matrix for an individual substorm event q centred

on the time of the substorm onset. τ is the time elapsed since the substorm

onset. The aggregate response matrix for the set of substorms is then,

Akl(τ) = 116 ∑ q=1 A∗_kl(q)(τ) M ∑ q=1 A∗∗_kl(q)(τ) . (3.6)

likelihood for pair k,l during a substorm event.

In figure 3.10 we plot the aggregate network parameters for the average substorm. The parameters have the same meaning, broadly speaking, as those

in section 3.1.1 but differ in their normalisation. The average connection

distanceδ is now, δ(τ) = Ng ∑ k=1,k̸=l Ng ∑ l=1,l̸=k M ∑ q=1 A∗_kl(q)(τ)δkl Ng ∑ k=1,k̸=l Ng ∑ l=1,l̸=k M ∑ q=1 A∗∗_kl(q)(τ)δkl , (3.7)

whereNg is the number of grid cells. It is important to note that the value of δ for the aggregate response can not be directly equated to that used for the test case substorms.

The explicit forms of other parameters are given in 4. In figure 3.11 we

show the network maps for two selected times,τ = 44 mins andτ = 110 mins.

For these maps we split the the degree into short (δkl < 4000km) and long

range (δkl >4000km) (see chapter 4 for explicit definitions). The connection

maps are constructed by considering only connections that are connected in at least 35% of the 116 substorm events. The connections plotted are split into

long and short range connections. The aggregate network response shares

some similar features to the results for the test case substorms. There is a significant increase in the connection likelihood shortly after the onset of the substorms. Unlike the test case substorms there is not a dominant high latitude network response at the onset, on the contrary the low latitude connections appear to dominate the network. The α, δ, θh,l,c responses all exhibit a two

peak structure, with the peak closer to onset being smaller in magnitude. The increased average degree at the second peak indicates an increasingly global

Figure 3.10: The network parameters for the aggregate network response to a set of 116 isolated substorms. Plotted from top to bottom isα, the average connection likelihood for the entire network,δthe average connection distance,θh,l,cthe average connection likelihood for connections between high latitude grid cells (green), low latitude grid cells (blue), and connections between high and low latitude grid cells. AE (blue), AU (green) and AL (red) are averaged over the 116 substorm events. Highlighted are two times (τ = 44 andτ = 110) in which we show the network maps in figure 3.11.

Figure 3.11: Snapshots of the correlation network maps for the aggregate network response to substorms at timesτ = 44 andτ = 110, highlighted in figure 3.10. The figure is organised as follows: Left - the connection maps. Only connections where

Akl>0.35 are plotted. Centre - the short range degree which quantifies the extent of connection between a particular region and all of its close neighbours (regions within 4000 km of each other). Right - the long range degree which quantifies the extent of connection between a given region and all other distant regions (regions greater than 4000 km away from each other). The contour values represent the % likelihood that a given region is connected to any other region in its network domain. The redder the contour the greater the increase in degree. The black dotted concentric circles represent the MLat contours. They are from outer to inner 50◦, 58◦, 66◦, 74◦ and 82◦ MLat contours.

connection structure during the recovery phase.

Importantly, a visual inspection of the connection map atτ = 44 shows

that there is a very similar connection pattern to that found at time (2) in figure 3.2. The largest increase in short range degree is also found at high latitudes around 23 hours MLT, this is where the average location in which

a substorm onset occurs [Gjerloev et al., 2007]. At τ = 110 the region of

enhanced short range correlation at high latitude has expanded. In addition there is now a significant number of long range connections at low latitudes

between dayside and nightside sectors. This bears resemblance to time (4) in figure 3.2 for the test case substorms. AE, AU, and AL at this point indicate that we are in the recovery phase for the majority of the substorm events. This gives further evidence to the idea that the system relaxes coherently on a global scale during the recovery phase.