# Recent developments

## 2021​

Reconstructing Substorms via Historical Data Mining: Is It Really Feasible?
N. A. Tsyganenko, V. A. Andreeva, M. I. Sitnov, G. K. Stephens, J. W. Gjerloev, X. Chu, O. A. Troshichev

Abstract (click on the arrow)

The evolution of the low-latitude magnetosphere over the substorm cycle is reconstructed based on a new high-resolution 3D representation of the magnetic field and nearest-neighbor data mining. The study covers radial distances $2.5-25~R_E$ and employs a record-large pool of spacecraft data taken during 1995-2019. The magnetospheric state is quantified by four indices, representing the ground geomagnetic activity and its temporal trends in the entire range of geomagnetic latitude: the SuperMAG SMR, the midlatitude positive bay MPB, the auroral SML, and the polar cap PC index. The developed technique has been tested on specific substorm events, with the results presented in the form of 5-min cadence diagrams and animations of the magnetic field line configurations and electric current distributions. In all the analyzed events, the initial intensification and radial expansion of the inner tail current is accompanied by a gradual stretching of the magnetic field, followed by its sudden collapse, dramatic depletion of the current beyond $R\sim 12~R_E$, and a large-scale dipolarization of the field around the time of MPB peak, after which the system recovers and tends to its pre-substorm state.

(Journal of Geophysical Research Space Physics, Vol. 126, 2021)

Reconstruction of Magnetospheric Storm-Time Dynamics Using Cylindrical Basis Functions and Multi-Mission Data Mining
N. A. Tsyganenko, V. A. Andreeva, M. I. Sitnov

Abstract (click on the arrow)

First results are presented of the modeling of magnetospheric storm events, based on: (i) a new method to represent the magnetic field by means of the so-called cylindrical basis functions, (ii) the data mining approach by Sitnov et al. (2008), and (iii) upgraded and extended pool of multi-mission data taken in 1995-2019. The study is focused on the low-latitude magnetospheric domain in the distance range $3-18~R_E$ bounded by field line shells with footpoint latitudes $\pm 70^{\circ}$. The magnetic configurations are reconstructed from data subsets, selected from the grand database by the nearest-neighbor method, using both interplanetary data and the ground disturbance indices. A strong storm of May 27-29, 2017, has been studied in relation to its effect on the reconfiguration of the low-latitude magnetosphere. The modeling reproduces the main features of the magnetosphere dynamics in terms of the geomagnetic field depression/compression and extremely variable field line stretching. The initial contraction of the magnetosphere during the storm sudden commencement results in a local transient surge of the inner tail current and a dramatic antisunward discharge of the magnetic flux. As the storm progresses, the ring current buildup results in a strongly depressed magnetic field in the inner magnetosphere, which expels the magnetic flux to larger distances and increases the field line connection across the more distant tail plasma sheet. At the same time, a strong dawn-dusk asymmetry is developed due to the formation of the duskside partial ring current, in agreement with previous independent results.

(Journal of Geophysical Research Space Physics, Vol. 126, 2021)

Data-Based Modeling of the Earth's Magnetic Field
N. Tsyganenko, V. Andreeva, M. Kubyshkina, M. Sitnov, G. Stephens

Summary (click on the arrow)

This chapter addresses the empirical models of the terrestrial magnetosphere based on large amounts of spacecraft data from many past and present satellite missions. Unlike computer simulations, which derive the expected magnetospheric configurations by solving first-principle equations, the data-based models seek to reconstruct the real-world magnetosphere from direct in situ observations and, in that sense, represent the "ground truth" of the data. The empirical models are based on three cornerstones: multiyear archives of satellite and ground data, a mathematical framework describing the magnetospheric field sources, and parametrization methods relating the model input to the solar wind drivers and/or ground-based geomagnetic indices. Accordingly, this chapter includes three sections devoted to each of the above aspects. In conclusion, we discuss future prospects and challenges, with a particular focus on reconstructing instantaneous real-time magnetospheric configurations, based on simultaneous data of multisatellite constellations of the geospace monitors.

(Magnetospheres in the Solar System, Chapter 39, eds: R. Maggiolo, N. André, H. Hasegawa, D. T. Welling, Y. Zhang and L. J. Paxton, 2021)

## 2020​

Magnetospheric 'penetration' of IMF By viewed through the lens of an empirical RBF modeling
N. A. Tsyganenko, V. A. Andreeva

Abstract (click on the arrow)
The spiral structure of the interplanetary magnetic field (IMF) is known to induce intra-magnetospheric azimuthal magnetic field By which strongly correlates with the IMF By. We reconstruct this effect for the first time in 3D, using a large set of data taken in the near/inner magnetosphere and a flexible magnetic field model based on expansions in radial basis functions (RBF). The RBF model serves here as a magnifying glass with tunable resolution, focused on the specific region of interest. In this study, we used it to explore the IMF-induced By both on a global scale (i.e., for the entire range of local times) and in the night sector only, to better visualize details in the region with the strongest `penetration' magnitude. The induced By was found to maximize on the nightside at distances R~10-12Re, where it concentrates around the solar magnetic equator and bifurcates into a pair of peaks located in pre-dawn and post-dusk sectors. The By penetration is associated with the IMF-induced asymmetry of field-aligned currents at the plasma sheet boundary. Even on a statistical level, the peak values of the induced By can substantially exceed the external IMF By. The effect is significantly stronger under southward IMF Bz conditions and grows with increasing geodipole tilt angle. This work was supported by the Russian Foundation for Basic Research (RFBR) grant 17-05-00415.

(Journal of Geophysical Research Space Physics, Vol. 125, 2020)

## 2019​

Empirical modeling of the geomagnetosphere for SIR and CME-driven magnetic storms
V. A. Andreeva, N. A. Tsyganenko

Abstract (click on the arrow)
During geomagnetic disturbances, the solar wind arrives in the form of characteristic sequences lasting from tens of hours to days. The most important magnetic storm drivers are the coronal mass ejections (CMEs) and the slow-fast stream interaction regions (SIRs). Previous data-based magnetic field models did not distinguish between these types of the solar wind driving. In the present work we retained the basic structure of the Tsyganenko and Andreeva (2015) model but fitted it to data samples corresponding to (1) SIR-driven storms, (2) CME-driven storms preceded with a shock ahead of the CME, and (3) CME-driven storms without such shocks. The storm time dynamics of the model current systems has been represented using the parametrization method developed by Tsyganenko and Sitnov (2005), based on dynamical variablesWi, calculated from concurrent solar wind characteristics and their previous history. The database included observations of THEMIS, Polar, Cluster, Geotail, and Van Allen Probes missions during 155 storms in 1997-2016. The model current systems drastically differ from each other with respect to decay rate and total current magnitudes. During SIR-induced storms, all current systems saturate, while during CME-induced disturbances, the saturation occurs only for the symmetric ring current and the tail current. The partial ring current parameters are drastically different between SIR- and CME-induced storm sets. In the case of SIR-driven storms, the total partial ring current is comparable with symmetric ring current, whereas for all CME-induced events it is nearly twice higher. The results are compared with GOES 15 magnetometer observations. This work was supported by the Russian Science Foundation grant 14-17-00072.

(Journal of Geophysical Research Space Physics, Vol. 124, 5641-5662, 2019)

Secular shift of the auroral ovals: How fast do they actually move?
N. A. Tsyganenko

Abstract (click on the arrow)
A surprisingly fast secular drift of the Northern geomagnetic dip pole during the last two decades has attracted much interest lately, in particular, evoking speculations about a possibility of a sweeping relocation of the auroral oval. This letter presents first results of a model investigation of this issue, based on an empirical representation of the distant magnetosphere combined with a series of internal geomagnetic field models for 12 epochs, covering the interval from 1965 through 2020. The secular drift of the Northern auroral oval was found to result in its net displacement over the 55-year period, commensurate with the concurrent shifts of the centered, eccentric, and corrected geomagnetic poles, all of them much smaller than the enormous spurt of the Northern dip pole. In the Southern Hemisphere, the shift of the auroral oval and of the poles over the same period is much weaker, revealing a remarkable interhemispheric asymmetry. This work was supported by the Russian Foundation for Basic Research (RFBR) grant 17-05-00415.

(Geophysical Research Letters, Vol.46, pp.3017-3023, 2019)

## 2018​

Empirical modeling of dayside magnetic structures associated with polar cusps
N. A. Tsyganenko, V. A. Andreeva

Abstract (click on the arrow)
The magnetic structure of dayside polar cusps is intimately related to the high-latitude field-aligned currents (FACs) and the cross-B diamagnetic currents due to the penetrated plasma of magnetosheath origin. The dayside FAC configuration is sensitive to the azimuthal component of the interplanetary magnetic field, manifested in the latitudinal splitting and longitudinal overlapping of the Region 1 FAC zone around noon. The diamagnetism of the polar cusp plasma results in deep cleft-shaped depressions of the ambient magnetic field. Neither of the above factors have yet been properly addressed in the existing empirical models of the distant magnetosphere. To fill this gap, an advanced data?based model has been developed, including the spiral structure of the dayside FACs and their splitting/overlapping in response to the orientation and magnitude of the azimuthal interplanetary magnetic field component By. The cusp diamagnetic field depressions are modeled using a new approach, based on a 3D system of magnetic “bubbles” (Tsyganenko & Andreeva, 2018, https://doi.org/10.1029/2018GL078714). The magnetic effects associated with FACs and diamagnetic currents are represented within the framework of a single hybrid model, fitted to large subsets of spacecraft data. The obtained results are analyzed in the context of the dayside magnetic field response to interplanetary conditions and the geodipole tilt angle. Published in JGR-A, October 27, 2018 This work was supported by the Russian Foundation for Basic Research grant 17-05-00415.

(Journal of Geophysical Research Space Physics, Vol. 123(11), pp.9078-9092, 2018)

Building the magnetosphere from magnetic bubbles
N. A. Tsyganenko, V. A. Andreeva

Abstract (click on the arrow)
A new approach has been developed to reconstruct the magnetospheric configurations from data by directly representing the magnetic field as a sum of divergence-free contributions from a set of diffuse bubble-like field sources, more or less evenly distributed over the modeling region. Unlike the earlier suggested method based on the radial basis functions, the new fully local approach does not involve toroidal and poloidal fields, which makes it conceptually simpler and computationally more straightforward. The method has been tested on artificial data sets generated using an empirical model and a global magnetohydrodynamic simulation. The new model was shown to faithfully reconstruct the high-latitude magnetospheric structures, such as the field-aligned currents and the diamagnetic depression in the outer polar cusp funnels. The new method can serve as a flexible tool with a tunable resolution and varied focus area, to be used in the data-based modeling of the magnetosphere.

This work was supported by the Russian Foundation for Basic Research, grant 17-00-00415.

(Geophysical Research Letters, Vol.45(13), pp.6382-6389, 2018)

## 2017​

Empirical modeling of the quiet and storm-time geosynchronous magnetic field V. A. Andreeva and N. A. Tsyganenko

Abstract (click on the arrow)
A dynamical empirical model of the near-geosynchronous magnetic field has been constructed, based on a recently developed RBF approach and a multi-year set of spacecraft data taken by THEMIS, Polar, Cluster, and Van Allen Probes missions including 133 geomagnetic storms in the time interval between 1996 and 2016. The model describes the field as a function of Cartesian solar-magnetic coordinates, dipole tilt angle, solar wind ram pressure, and of a set of dynamic variables representing the response of the magnetosphere to the external driving/loading during the active phase of a space weather event, followed by the internal relaxation/dissipation during the storm recovery. In terms of the disturbance level, the model's validity range extends to intense storms with peak Sym-H values down to -150 nT. The spatial validity domain is a toroidal volume bounded by the inner (L ≈ 4) and outer (L ≈ 9) dipolar L-shells, which allows the model to be used for tracing field lines to magnetically map geosynchronous spacecraft locations down to low altitudes. The model has been validated on independent out-of-sample magnetic field data and compared with an earlier empirical model and GOES-15 data taken in 2012 and 2015.

This work was supported by Russian Foundation for Basic Research grant 17-05-00415

(Geophysical Research Letters, Vol.45(13), pp.6382-6389, 2018)