Electrodynamic Parameters of the Auroral Oval from Combined Spacecraft and Ground Measurements

RESUME Spacecraft traversing the auroral oval respond primarily to the field-aligned currents at its poleward and equatorward borders that are part of a solenoidal current system. If electric and magnetic field measurements are done, it is possible to determine the integrated Pedersen conductivity of the auroral oval. On the ground, however, one detects primarily the magnetic effects of the Hall currents associated with the auroral oval electric field. If the Hall current can be determined, along with the electric field, one can obtain the Hall conductivity. Inversion of magnetic perturbations in the meridian traversed by the spacecraft can give the Hall current. The Automated Forward Modelling (AFM) method permits this to be done effectively. The method is described with an example based on FAST over the Churchill meridian in Canada. Studying temporal and spatial variations needs multiple instrumented meridians and spacecraft. Efforts to increase the number of instrumented meridians in Canada are described. 1. MAGNETIC AND ELECTRIC PERTURBATIONS IN THE AURORAL OVAL The basic nature of the current systems in the auroral oval has been well established for about 50 years. Much of the electrodynamics is controlled by electric fields associated with magnetospheric convection. These point generally equatorward in the morning sector and poleward in the evening sector. The anisotropic ionosphere responds to these imposed electric fields with Pedersen currents, following the E field projection, and Hall currents, perpendicular to E and B (which is essentially vertical). Closure of the current systems is by field-aligned currents (FAC), which are generally local to close the Pedersen currents, and may be distant to close the Hall currents, which are often of large longitudinal extent. The closed north-south system associated with Pedersen currents is essentially solenoidal and produces little perturbation outside of the three-dimensional system bounded by current sheets. Notably, on the ground the perturbations due to the Pedersen system are small. In addition, a satellite outside of the auroral zone detects little effect from this system. However, when it traverses the bounding currents, large offsets from baseline levels are seen. The Hall system has in some ways the converse magnetic effect. Its perturbations are readily detected on the ground, which is only roughly 100 km below the relatively nonsolenoidal Hall ionospheric currents. Since Hall flow is often largely east-west, the main effects detected on the ground are in the X (geographic northward) component and the Z (vertically downward) components. Since satellites generally pass several hundred (often 700) or more kilometers above the ionosphere, the Hall current effects at satellite altitude are usually not pronounced. For completeness it should be noted that the direct detection of the FAC whose locally unbalanced parts are associated with the Hall system is possible: their magnetic effects at low latitude are referred to as “low-latitude bays” and observed mainly in the X and Y (eastward) components. During active times the usual configuration is to have downward FAC east of midnight, an ionospheric westward Hall current traversing the midnight or late evening sector, and upward FAC to the west. This delineates the “substorm current wedge” associated with substorm onset, which will not be discussed further here. Although other techniques (notably radars) can be used to determine ionospheric parameters, the discussion here will focus on in-situ direct measurement of auroral zone E fields and the relation to currents through conductivity. A current dataset of interest is that of nearly ten years from the FAST satellite [1]. The Canadian e-POP project [2] should provide relevant measurements in the next couple of years. After that, and relevant here, the Canadian Electric Field Instrument on Swarm will mean that E and B field measurements will be available. The satellite measurements alone can be used to determine the Pedersen current and the relation of E to B allows determination of the integrated Pedersen conductivity of the ionosphere. To determine the Hall conductivity, however, requires that the Hall current be determined, and as indicated above, ground measurements respond to the Hall current more than do most satellites. We must therefore consider how to combine ground and satellite data to obtain all of the electrodynamic parameters of the auroral ionosphere by direct measurement. 2. AUTOMATED FORWARD MODELLING (AFM) Interpretation of ground magnetic data is difficult, even if the data come from the same magnetic meridian. Examples of magnetic data from many locations are common in the literature, or one may examine the solid lines in Fig. 1. These show perturbations from the CANOPUS stations of the Canadian Churchill meridian on June 3, 1997. The data were carefully baselined by using quiet days throughout 1997. Only the X and Z components are used in single meridian modeling, so the Y component is not shown. It is clear that an auroral event (onset) with accompanying currents took place very close to 6 UT on this day. The perturbations seem maximal near FCC (Fort Churchill), so that the centre of the onset must have been near there. This is borne out by the change in sign of the Z component. Negative X perturbations arise from westward ionospheric currents over the station; the placement of the station with respect to the current determines the sign of Z. For a westward current, Z is positive as observed north of the electrojet, and negative south of it. The near-zero Z perturbations at FCC, along with the +Z perturbations north of it, and the –Z perturbations south of it, support the conclusion that the currents were centred near this station. We can note the duration of the event and that there was some precursory activity. Importantly, this is about all that a skilled interpreter can deduce from what is in fact a fairly complete dataset for the meridian. Figure 1. Magnetic X and Z component perturbations in the Canadian Churchill meridian on June 3 1997. Lines represent data, black for the X component, blue for the Z component. Red dots correspond to X model output once parameters were optimally adjusted, and blue dots to Z model results. To go further, a quantitative method of inversion of the magnetic data is needed. Approaches based on potential functions are possible [3]. The technique used here, Automated Forward Modelling, proposes a forward model of current systems which could give rise to the magnetic perturbations observed. The parameters in that model are varied in such a way that the deviation between the observed magnetic fields and those predicted by the model are reduced. In the ideal case, the parameters can be chosen to correspond to simple physical parameters associated with the current system. A forward model can be made using the Biot-Savart law in combination with Earth induction, by specifying where currents flow in space and the ionosphere [4][5]. Adjustment of the parameters specifying the current system can be done until the match to the input data is optimal. In principle, arbitrarily complex current systems may be described in three dimensions in nearEarth space and their parameters determined. In practice, available magnetic data is sparse and welldetermined solutions can be difficult to obtain. Figure 2. By varying the current (large horizontal arrow) and latitudinal boundaries (small vertical arrows) an optimal match of model results and data can be made and these physical parameters determined. Field-aligned currents may be included (as shown at ends of ionospheric current flow region). The optimum situation can be found when data from meridian chains is available, since in many cases a simple model involving an electrojet flowing across the meridian chain is physically realistic, and in this case there is a good ratio of data available to number of parameters to be determined. From meridian chain data a forward modeling procedure can give the current across the meridian and the latitudes between which it flowed. In this way the many data points specifying the magnetic perturbations along a meridian can be reduced to three simple parameters, which have an easily understood physical significance. For efficient processing of large amounts of magnetic data, the matching process can be automated. In the Automated Forward Modeling (AFM) procedure this is done using the Levenberg-Marquardt algorithm [6]. A schematic of the variables involved and the way in which they are varied is shown in Fig. 2. Detailed descriptions of the AFM procedure are given elsewhere [7][8]. Fig. 3 shows the results of applying a fully automated (i.e. no special starting conditions used) version of AFM to the dataset of Fig. 1, for the period of interest near the time of substorm onset. This allows a clear identification of the slightly disturbed period before onset as having typical growth phase behaviour of equatorward motion of the electrojet boundaries. In addition, it may be seen that the current across the meridian smoothly strengthened during the growth phase, which has been identified between two vertical lines. The onset is seen to have taken place well poleward of the region of growth phase currents. Following onset, the poleward border of the electrojet moved rapidly poleward, a well established behaviour, and the current continued to rise. The unusual activation of a region well poleward of the growth phase region could be confirmed in this case by inspection of POLAR spacecraft images. What is important to note here is that the inversion made obvious what the stacked magnetograms did not: the growth phase currents and the unusual onset location. In addition, the three parameters needed to describe the electrojet are available as physical quantities in numerical form. Figure 3. ModellingGrowth phase and onset of a substorm on June 3