Real-time simulation of the geoelectric field spatiotemporal evolution due to geomagnetic disturbances

We present a methodology that allows real-time simulation of the geoelectric field (GEF) spatiotemporal evolution in a given 3-D conductivity model of the Earth based on continuously augmented inducing source data. The presented concept is validated using Fennoscandia as a test region. The choice of Fennoscandia is motivated by several reasons. First, it is a high latitude region, where the GEF is expected to be particularly large. Second, there exists a 3-D ground electrical conductivity model of the region. Third, the regional magnetometer network, IMAGE, allows us to build a realistic model of the source for a given geomagnetic disturbance. Taking the 7-8 September 2017 geomagnetic storm as a space weather event, we show that real-time high-resolution 3-D modeling of the GEF is feasible and requires only a few tens of seconds.

Real-time simulation of the geoelectric field spatiotemporal evolution due to geomagnetic disturbances Elena Marshalko (1), Mikhail Kruglyakov(2), and Alexey Kuvshinov (3) (1)Finnish Meteorological Institute, Helsinki, Finland; (2)University of Otago, Dunedin, New Zealand; (3)Institute of Geophysics, ETH Zurich, Switzerland The presented concept is validated using Fennoscandia as a test region. The choice of Fennoscandia is motivated by several reasons. First, it is a high latitude region, where the GEF is expected to be particularly large. Second, there exists a 3-D ground electrical conductivity model of the region. Third, the regional magnetometer network, IMAGE, allows us to build a realistic model of the source for a given geomagnetic disturbance.
Taking the 7-8 September 2017 geomagnetic storm as a space weather event, we show that real-time high-resolution 3-D modeling of the GEF is feasible and requires only a few tens of seconds.

SECS METHOD
Spherical Elementary Current Systems (SECS) form a set of basis functions for representing 2-D vector fields on a spherical surface [Vanhamäki and Juusola, 2020].
-In this study we use a modification of this method with separation of the measured magnetic field into external and internal parts. It is assumed that currents flow in two shells: 1. Above the Earth to approximate the external source 2. Below the surface of the Earth to account for the EM induction -Actual currents are obtained by fitting of the observed magnetic field.
Source of magnetic field data: IMAGE magnetometer array.
Magnetic field data cadence: 10 s.

PRINCIPAL COMPONENT ANALYSIS
Principal component analysis (PCA) is a dimensionality-reduction method that is often used to reduce the dimensionality of large data sets, by transforming a large set of variables into a smaller one that still contains most of the information in the large set .
Here j (t,r) is the equivalent ionospheric current, t is time, r is a position vector, c (t) are timedependent coefficients, j (r) are time-independent spatial modes (principal components), L is the number of spatial modes.
According to the PCA, 99% of the variability of the SECS source during the considered event can be described using L=21 spatial modes. Our standard approach: 1. The inducing source j (t,r) is transformed from the time to frequency domain using the Fourier transform 2. Maxwell's equations in the frequency domain are numerically solved for the corresponding frequencies ω using 3-D EM modeling code PGIEM2G based on the volume integral equation approach [Kruglyakov and Kuvshinov, 2018] where μ is the magnetic permeability of free space; ω is angular frequency; B(r,ω;σ), E(r,ω;σ) are magnetic and electric fields, respectively. σ(r) is the spatial distribution of electrical conductivity. 3. Electric field E(t,r) and magnetic field B(t,r) in the time domain are obtained by means of the inverse Fourier transform.

Real-time electric field modeling:
1. Precompute electric field E (r ,ω;σ) for selected PCA-recovered spatial modes for a set of frequencies using PGIEM2G 2. Calculate convolution integrals: 3. Calculate electric field in the time domain using following convolution integrals: c (t-τ) are obtained using the PCA of the SECS source and can be a continuously augmented nowcasted or forecasted time series.
Electric field at a time step t will be calculated based on the data for the previous time segment of length T. According to out analysis T=15 min is a reasonable choice (see Figure 4).