# Has Anyone Looked?

Visual intuition for field-aligned currents and spatial autocorrelation in ground magnetometer data

## Lesson 1: Project Overview

### 1. The magnetosphere as habitat

The solar wind — a supersonic flow of charged particles from the Sun — slams into Earth's magnetic field and carves out a cavity called the magnetosphere. On the dayside, the field is compressed. On the nightside, it stretches into a long magnetotail extending millions of kilometers antisunward.

Inside this cavity, charged particles are trapped on magnetic field lines, bouncing between hemispheres. The plasma sheet in the magnetotail is a reservoir of hot plasma. The question driving this project: is there persistent spatial structure in the magnetosphere beyond what the known current systems produce?

Figure 1. Schematic magnetosphere. The solar wind compresses the dayside and stretches the nightside into a long tail. Blue = closed dipole field lines; red = open lines dragged into the tail.

### 2. Ground magnetometers as sensors

The SuperMAG collaboration maintains a network of ~500 ground magnetometer stations worldwide. Each station measures the local magnetic field perturbation caused by currents flowing in the ionosphere (~100-300 km altitude) and along magnetic field lines connecting the ionosphere to the magnetotail.

This project uses 48 nightside stations in the auroral zone (roughly 55-75 degrees magnetic latitude). They sit under the region where magnetotail dynamics map to ionospheric currents. The Scandinavian cluster is particularly dense.

Figure 2. Schematic polar view of nightside auroral-zone stations. The green dashed band is the auroral oval. The dense Scandinavian cluster sits at the R1/R2 boundary latitude.

### 3. Moran's I: measuring spatial autocorrelation

Moran's I quantifies whether nearby stations show similar perturbations (positive I, spatial clustering), random variation (I near zero), or anti-correlated signals (negative I, checkerboard pattern). It is computed from the station values weighted by a spatial weight matrix (inverse-distance or threshold-based).

Bruce found persistent positive Moran's I in nightside ground magnetometer data, but only when AE exceeds ~100 nT (moderate geomagnetic activity). Below that threshold, the spatial pattern vanishes into noise. This is not trivially expected.

Figure 3. Three spatial patterns and their Moran's I values. (a) Clustered: nearby points have similar values (I > 0). (b) Random: no spatial structure (I ~ 0). (c) Checkerboard: nearby points differ systematically (I < 0). The nightside magnetometer data consistently shows pattern (a).

### 4. The key question

The spatial clustering Bruce observes could have two very different origins. The first is mundane: the well-known field-aligned current (FAC) system creates a latitude-dependent pattern on the ground, and the weight matrix (based on station separation) naturally picks this up. In this case, the spatial autocorrelation is just an artifact of known FAC geometry.

The second possibility is more interesting: the spatial pattern reflects genuine self-organized structure in the magnetotail plasma sheet that is not fully explained by the R1/R2 current system. Distinguishing these two is the central scientific question.

Is the persistent Moran's I in nightside magnetometer data just the ground signature of the R1/R2 field-aligned current system? Or does it contain a component from magnetotail self-organization?

Figure 4. Two possible explanations for persistent Moran's I. Left: spatial autocorrelation is an artifact of the latitude-banded R1/R2 FAC system. Right: spatial clusters have emergent structure that crosses latitude bands, suggesting magnetotail self-organization.

## Lesson 2: FAC Discriminating Tests

### 1. Field-aligned currents (R1/R2)

Region 1 (R1) currents flow along magnetic field lines at ~68-75 degrees MLAT (the poleward edge of the auroral oval). Region 2 (R2) flows at ~58-68 degrees (the equatorward edge). R1 connects magnetopause currents to the ionosphere; R2 connects the ring current. In the premidnight sector, R1 flows into the ionosphere and R2 flows out; this polarity reverses post-midnight.

These two current sheets are the dominant organized current system on the nightside. If the observed Moran's I is simply seeing R1/R2, then the spatial pattern has a well-understood origin and no mystery remains.

Figure 5. The R1/R2 field-aligned current system. R1 (blue) connects magnetopause currents to the poleward auroral zone; R2 (red) connects ring current to the equatorward zone. Hall and Pedersen currents close the circuit horizontally in the ionosphere. A ground magnetometer senses all of these.

### 2. Ground signature of FACs

A crucial seasonal asymmetry: in winter darkness, ionospheric conductivity is low (no solar EUV), so Hall and Pedersen currents are weak. The ground magnetometer primarily senses the FAC pattern directly. In summer, strong Hall currents dominate the ground signal, redistributing the magnetic perturbation horizontally (Laundal et al. 2015).

The Z (vertical) component of the ground field is a particularly direct FAC proxy because a vertical current creates circular horizontal B-field lines, and the Z-component captures the local vertical field distortion of a nearby FAC (Weimer 2010). The H (horizontal) component mixes FAC and ionospheric current contributions.

Figure 6. A downward FAC (blue arrow) distorts the local magnetic field. At a nearby ground station, the Z (vertical) component captures the direct FAC signature (strong), while the H (horizontal) component mixes FAC and ionospheric current contributions (weaker, more ambiguous).

### 3. Test 2 results: Z vs H

If FACs are the primary source of the spatial pattern, then the Z-component (direct FAC proxy) should show stronger spatial autocorrelation than the H-component (which mixes FAC with Hall currents). This is exactly what the data show.

Test 2 result: Z-component Moran's I exceeds H-component in 71% of months. Mean I_Z = 0.234, mean I_H = 0.161, mean I_N = 0.103. This supports FAC as the dominant source of the spatial pattern.

Seasonal surprise: the Z > H dominance holds strongly in both summer (~77%) and winter (~77%), but weakens at equinox (~57%). This was unexpected — the naive prediction was that winter (low conductivity, direct FAC sensing) would show the strongest Z dominance.

Figure 7. Moran's I by magnetic field component and season. The Z-component (direct FAC proxy) consistently shows the strongest spatial autocorrelation. Z exceeds H in 71% of all months, with the Z > H dominance equally strong in summer and winter (~77%) but weaker at equinox (~57%).

### 4. Test 4 results: Latitude structure

If the R1/R2 system creates the spatial pattern, then stations in the same latitude zone should be more correlated with each other than with stations in different zones. The data confirm this: same-zone station pairs have mean correlation r = +0.26, while cross-zone pairs have r = +0.14.

The R1/R2 boundary zone (63-68 degrees MLAT, heavily populated by the Scandinavian cluster) shows the strongest same-zone correlation. This is exactly where FAC gradients are sharpest — the boundary between poleward R1 and equatorward R2 currents.

Test 4 result: Same-zone r = +0.26 vs cross-zone r = +0.14. Boundary zone (Scandinavian cluster, 63-68° MLAT) has strongest intra-zone correlation. Consistent with FAC geometry dominating the spatial pattern.

Figure 8. Latitude zone structure in station correlations. Thick colored lines = same-zone pairs (higher correlation). Thin dashed lines = cross-zone pairs (lower correlation). The R1/R2 boundary zone (purple, 63-68° MLAT, Scandinavian cluster) shows the strongest intra-zone correlation, consistent with FAC geometry.

### 5. What's next: CCMC decomposition

The definitive test requires simulation data. The Community Coordinated Modeling Center (CCMC) runs SWMF (Space Weather Modeling Framework) simulations that decompose the ground magnetic perturbation into four physical components: the FAC contribution, the Hall current contribution, the Pedersen current contribution, and the magnetospheric (MHD) contribution.

Computing Moran's I on each component separately would directly answer the question. If I_FAC alone accounts for most of the total spatial autocorrelation, the mystery is resolved: the pattern is just known FAC geometry. If significant spatial structure remains in the residual (total minus FAC), that points to self-organization.

Figure 9. The SWMF decomposition test. The total ground dB is split into FAC, Hall, Pedersen, and MHD components. Computing Moran's I on each component separately determines whether the FAC component alone explains the observed spatial autocorrelation, or whether residual structure points to magnetotail self-organization.

Tutorial created 2026-04-21. All SVGs are inline, no external dependencies. Page works offline.