Growth-phase $B_z$ hump conditions and the quantitative fidelity of data-mining-based global empirical reconstructions of magnetospheric substorms

The first global empirical reconstruction of substorm current systems by data mining of multi-mission magnetometer archives (Stephens et al., 2019, the SST19 proof of principle) left a precisely identified set of unresolved discrepancies between the reconstruction, in situ observations, and MHD/kinetic simulations: systematic underestimation of current-sheet thinning and dipolarization magnitudes; uninvestigated weighting of the nearest-neighbor distance metric; unknown formation conditions and tail location of the late-growth-phase equatorial $B_z$ hump (flux pileup with a tailward $B_z$ gradient); and no separate region-2-sense field-aligned current earthward of the substorm current wedge, contrary to simulation predictions. Later work by the same group has resolved parts of this agenda (global X-line structure, the 26 February 2008 weak-driving test event, multi-index state vectors, growth-phase validation against low-altitude precipitation, cislunar-tail flux accumulation), but a definitive characterization of the conditions and location of growth-phase flux accumulation, the systematic amplitude underestimation, and the missing region-2 precursor current all remain open. The problem is to determine the conditions favorable for the formation of the late-growth-phase $B_z$ hump and what fixes its location in the tail, to explain and, where possible, reduce the systematic underestimation of thinning and dipolarization magnitudes relative to in situ data, and to establish whether the simulation-predicted region-2-sense precursor current exists in the empirical data, thereby obtaining a quantitatively faithful empirical picture of substorm current systems.

Background

A magnetospheric substorm is the quasi-periodic explosive release of energy stored in Earth's magnetotail: the nightside magnetic field stretches antisunward during a growth phase (~1 hour), then rapidly contracts earthward (dipolarization) as plasma is injected inward, producing auroral breakups and disturbances recorded by ground magnetometers. The $AL$ index — the lower envelope of deviations of the northward magnetic field at a chain of auroral-latitude observatories — is the classical scalar measure of substorm activity. During the growth phase the cross-tail current sheet thins (its magnetic signature is an increase of $|B_x|$, the tail-field component along the Sun–Earth line); at onset the current is diverted into the ionosphere along field lines, forming the substorm current wedge (SCW). Field-aligned currents (FACs) that connect the magnetosphere to the ionosphere come in two classical systems: region-1 (R1) FACs on the poleward side and region-2 (R2) FACs equatorward of them, the latter closing through the westward partial ring current. Empirical magnetic-field models of the Tsyganenko lineage (T89, TS05, TS07D) represent all these current systems by fitted analytical modules parameterized by solar-wind input and geomagnetic indices. Stephens et al. (2019) introduced a different, instance-based approach (termed SST19 in later work): instead of one universal model, for every moment of a chosen event a unique model is fitted to magnetometer data selected from a 1995–2017 multi-mission archive by a k-nearest-neighbor (kNN) rule in a 5-D state space built from the $AL$ index, its time derivatives, and a smoothed solar-wind electric field $vB_s^{IMF}$ (with $B_s$ the southward interplanetary magnetic field component). The reconstruction reproduced the global sequence of thinning, dipolarization, and SCW formation, and revealed in the late growth phase an equatorial 'Bz hump' — a local maximum of the northward equatorial field $B_z$ near $X \approx -16\,R_E$ in GSM coordinates ($X$ positive sunward, so the magnetotail lies at negative $X$; $R_E$ the Earth's radius) with a tailward $B_z$ gradient earthward of it, i.e. magnetic flux pileup ahead of onset. The reconstruction left the following items unresolved: (1) the magnitudes of thinning ($|B_x|$ increase) and dipolarization ($B_z$ spikes) are often underestimated relative to in situ data; (2) the sensitivity of the kNN distance metric to any single parameter is reduced by its 5-D dimensionality, and adjustment of weight factors has not been investigated; (3) the smoothed $vB_s^{IMF}$ parameter poorly captures weak or short growth phases, and the specific conditions favorable for the hump formation and determining its location in the tail remain to be investigated; (4) the method covers only conventional substorms with ~2-hour loading–unloading cycles, while longer steady magnetospheric convection (SMC) events — a quasi-steady mode in which dayside and nightside reconnection are balanced, defined from the same $AL$ and solar-wind parameters — would require customized averaging parameters; (6) the reconstruction (its Figure 10) shows no separate R2-sense current earthward of the SCW, although magnetohydrodynamic (MHD) and kinetic simulations (e.g. Birn et al., 1999, on flow braking and the SCW) predict such a precursor of dipolarizing flux tubes; and (7)–(8) the reconstruction's field-aligned current patterns have not been confronted with auroral imagery, and the model's high- and low-latitude FAC modules are labeled R1/R2 by latitude alone, leaving their true current-sense attribution open. (Item (5) — bursty bulk flows, dipolarization fronts, wedgelets, and other sub-grid phenomena — is not addressable by any global empirical reconstruction and is excluded from this problem's scope.) Of these items, the present problem addresses the open questions that remain unresolved: the formation conditions and tail location of the growth-phase $B_z$ hump, the quantitative underestimation of thinning and dipolarization magnitudes, and whether the additional R2-sense current system earthward of the substorm current wedge exists in the data and becomes part of the partial ring current. Documented limitations of the approach bear directly on these magnitudes: the method averages over substorms with different local-time distributions, smearing the singularly thin current sheet; the $AL$ index carries little information about the local-time location and extent of dipolarization and the substorm current wedge, which has motivated auroral indices such as SML; the smoothed $vB_s^{IMF}$ driver is a suboptimal proxy for thin-current-sheet development; and the dimensionality and weighting of the nearest-neighbor metric, along with the resolution of the model's basis functions, limit the sensitivity to these amplitudes.

Problem Statement

Within the framework of instance-based (k-nearest-neighbor) empirical reconstruction of the substorm-time magnetosphere from multi-mission magnetometer archives, resolve the following open questions left by Stephens et al. (2019): (a) determine the specific conditions favorable for the formation of the late-growth-phase equatorial $B_z$ hump (flux pileup with tailward $B_z$ gradient) and what determines its location in the tail, including its dependence on solar-wind driving strength and duration, extending beyond the case studies already published; (b) diagnose the cause of the systematic underestimation of current-sheet thinning ($|B_x|$ increase) and dipolarization ($B_z$ spike) magnitudes relative to in situ data, and determine whether these discrepancies can be reduced in a validated reconstruction; and (c) establish whether the additional region-2-sense (equatorward, partial-ring-current-closing) field-aligned current system earthward of the substorm current wedge, suggested by MHD and kinetic simulations of flow braking (Birn et al., 1999), exists in the empirical data — that is, whether it becomes part of the partial ring current — or whether its apparent absence is an artifact of insufficient spatial/temporal resolution. Resolution requires explaining the hump-formation conditions and location, the magnitude underestimations, and the presence or absence of the region-2-sense precursor current, consistently with magnetometer-based reconstructions and observations; whether the magnitude underestimations can be reduced is desirable but not required for resolution. Sub-grid small-scale phenomena — bursty bulk flows, dipolarization fronts, wedgelets — are excluded from this problem: they cannot be resolved by any global empirical reconstruction and must be studied with local observations and simulations.

References

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