Spherical Elementary Current System Method Research Articles

Comparing Three Approaches to the Inducing Source Setting for the Ground Electromagnetic Field Modeling due to Space Weather Events

AbstractGround‐based technological systems, such as power grids, can be affected by geomagnetically induced currents (GIC) during geomagnetic storms and magnetospheric substorms. This motivates the necessity to numerically simulate and, ultimately, forecast GIC. The prerequisite for the GIC modeling in the region of interest is the simulation of the ground geoelectric field (GEF) in the same region. The modeling of the GEF in its turn requires spatiotemporal specification of the source which generates the GEF, as well as an adequate regional model of the Earth’s electrical conductivity. In this paper, we compare results of the GEF (and ground magnetic field) simulations using three different source models. Two models represent the source as a laterally varying sheet current flowing above the Earth. The first model is constructed using the results of a physics‐based 3‐D magnetohydrodynamic (MHD) simulation of near‐Earth space, the second one uses ground‐based magnetometers’ data and the Spherical Elementary Current Systems (SECS) method. The third model is based on a “plane wave” approximation which assumes that the source is locally laterally uniform. Fennoscandia is chosen as a study region and the simulations are performed for the September 7–8, 2017 geomagnetic storm. We conclude that ground magnetic field perturbations are reproduced more accurately using the source constructed via the SECS method compared to the source obtained on the basis of MHD simulation outputs. We also show that the difference between the GEF modeled using laterally nonuniform source and plane wave approximation is substantial in Fennoscandia.

Dipolar elementary current systems for ionospheric current reconstruction at low and middle latitudes

The technique of spherical elementary current systems (SECS) is a powerful way to determine ionospheric and field-aligned currents (FAC) from magnetic field measurements made by low-Earth-orbiting satellites, possibly in combination with magnetometer arrays on the ground. The SECS method consists of two sets of basis functions for the ionospheric currents: divergence-free (DF) and curl-free (CF) components, which produce poloidal and toroidal magnetic fields, respectively. The original CF SECS are only applicable at high latitudes, as they build on the assumption that the FAC flow radially into or out of the ionosphere. The FAC at low and middle latitudes are far from radial, which renders the method inapplicable at these latitudes. In this study, we modify the original CF SECS by including FAC that flow along dipolar field lines. This allows the method to be applied at all latitudes. We name this method dipolar elementary current systems (DECS). Application of the DECS to synthetic data, as well as Swarm satellite measurements are carried out, demonstrating the good performance of this method, and its applicability to studies of ionospheric current systems at low and middle latitudes.

Field‐Aligned and Horizontal Currents in the Northern and Southern Hemispheres From the Swarm Satellite

AbstractWe present statistical investigation of the high‐latitude ionospheric current systems in the Northern Hemisphere (NH) and Southern Hemisphere (SH) during low (Kp < 2) and high (Kp ≥ 2) geomagnetic activity levels. Nearly 4 years of vector magnetic field measurements are analyzed from the two parallel flying Swarm A and C satellites using the spherical elementary current system method. The ionospheric horizontal and field‐aligned currents (FACs) for each auroral oval crossing are calculated. The distributions of the mean values of FACs as well as the horizontal curl‐free and divergence‐free currents in magnetic latitude and magnetic local time for each hemisphere and activity level are presented. To estimate the NH/SH current ratios for the two activity levels, we remove seasonal bias in the number of samples and in the Kp distribution by bootstrap resampling. This is done in such a manner that there are equal number of samples from each season in each Kp bin. We find that for the low activity level, the currents in the NH are stronger than in the SH by 12±4% for FAC, 9±2% for the horizontal curl‐free current, and 8±2% for the horizontal divergence‐free current. During the high activity level, the hemispheric differences are not statistically significant. This suggests that the local ionospheric conditions, such as magnetic field strength or daily variations in insolation, may be important and play a larger role during quiet than disturbed periods. This issue must be studied further.

Spherical Elementary Current Systems Method Applied to Geomagnetic Field Modeling for the Adriatic

The aim of this work was to derive an accurate regional model of geomagnetic components on the Adriatic. Data of north, east and vertical geomagnetic components at repeat stations and ground survey sites enclosing the Adriatic Sea were used to obtain a geomagnetic model at 2010.5 epoch. The core field was estimated by use of the global Enhanced Magnetic Model, while the crustal field by a mathematical technique for expanding vector systems on a sphere into basis functions, known as spherical elementary current systems method. The results of this method were presented and compared to the crustal field estimations by the Enhanced Magnetic Model. The maps of isolines of the regional model are also presented.

On Data Interpolation at Three Croatian Repeat Stations by Using the Spherical Elementary Currents Systems Method

A general mathematical tool for expanding vector systems on a sphere into basis functions, spherical elementary current system (SECS) method, was applied for separation of the geomagnetic field variations into external and internal parts, over a limited region of central and southeastern Europe. The registered variations at three Croatian repeat stations were compared to the variations estimated by the SECS method using the variations from the different sets of observatories. The results of the SECS method were also compared to a simple assumption that the variations at repeat station are equal to those at particular observatory. The relevance of this comparison was to get an insight about the possibility of using the SECS method for estimating the geomagnetic field variations over Croatia. The guidelines for the application of the SECS method for the purpose of reducing repeat station data were also given.

Data reduction of Croatian geomagnetic repeat stations surveys by using the spherical elementary current systems method

The geomagnetic declination, inclination and total field data surveyed at the Croatian Geomagnetic Repeat Stations Network were reduced to 2008.5, 2009.5 and 2010.5 epochs by a well-known observatory-based and a proposed method, in instances when an influence of the differences of secular variations at a repeat station and at an observatory were not taken into account. The motivation came from distances and distribution of the nearby geomagnetic observatories. A technique for expanding vector systems on a sphere into basis functions, known as the Spherical Elementary Current System (SECS) method, was applied to obtain separation of the geomagnetic field variations into external and internal parts, over Croatia and surrounding countries. The aim of this work is to propose the SECS method for determination of the annual mean values of north, east and vertical components of Earth’s magnetic field at the Croatian repeat stations. The results of the SECS method were compared to an observatory-based method which assumes that the variations of components about their annual mean values at a repeat station are equal to those at a particular nearby reference observatory. For reducing a repeat station data by this simple method the Furstenfeldbruck, Grocka and Tihany observatories were used, while for the SECS method additional three observatories were employed. The reduction methods were found comparable, while in the majority of instances the SECS method demonstrated smaller standard deviations of the components’ annual means. Besides, the annual mean values of the vertical component had the highest accuracies for both methods. The results indicate that the SECS method can be an acceptable method for data reduction to annual mean values.

Surface electric fields for North America during historical geomagnetic storms

To better understand the impact of geomagnetic disturbances on the electric grid, we recreate surface electric fields from two historical geomagnetic storms—the 1989 “Quebec” storm and the 2003 “Halloween” storms. Using the Spherical Elementary Current Systems method, we interpolate sparsely distributed magnetometer data across North America. We find good agreement between the measured and interpolated data, with larger RMS deviations at higher latitudes corresponding to larger magnetic field variations. The interpolated magnetic field data are combined with surface impedances for 25 unique physiographic regions from the United States Geological Survey and literature to estimate the horizontal, orthogonal surface electric fields in 1 min time steps. The induced horizontal electric field strongly depends on the local surface impedance, resulting in surprisingly strong electric field amplitudes along the Atlantic and Gulf Coast. The relative peak electric field amplitude of each physiographic region, normalized to the value in the Interior Plains region, varies by a factor of 2 for different input magnetic field time series. The order of peak electric field amplitudes (largest to smallest), however, does not depend much on the input. These results suggest that regions at lower magnetic latitudes with high ground resistivities are also at risk from the effect of geomagnetically induced currents. The historical electric field time series are useful for estimating the flow of the induced currents through long transmission lines to study power flow and grid stability during geomagnetic disturbances.

Interpolation of externally-caused magnetic fields over large sparse arrays using Spherical Elementary Current Systems

Abstract. A physically-based technique for interpolating external magnetic field disturbances across large spatial areas can be achieved with the Spherical Elementary Current System (SECS) method using data from ground-based magnetic observatories. The SECS method represents complex electrical current systems as a simple set of equivalent currents placed at a specific height in the ionosphere. The magnetic field recorded at observatories can be used to invert for the electrical currents, which can subsequently be employed to interpolate or extrapolate the magnetic field across a large area. We show that, in addition to the ionospheric currents, inverting for induced subsurface current systems can result in strong improvements to the estimate of the interpolated magnetic field. We investigate the application of the SECS method at mid- to high geomagnetic latitudes using a series of observatory networks to test the performance of the external field interpolation over large distances. We demonstrate that relatively few observatories are required to produce an estimate that is better than either assuming no external field change or interpolation using latitudinal weighting of data from two other observatories.

Characteristics of Magnetic Variations and Current Wedge in the Sawtooth Event on 30 September 2000

AbstractThe purpose of this paper is to study the response of auroral electrojets during the sawtooth event observed by LANL satellites on 30 September 2000. Firstly, we establish a method to determine large‐scale 2‐dimensional ionospheric equivalent current systems in the high‐latitude ionosphere using the spherical elementary current system method. Then we apply this method and magnetic data of high‐latitude magnetometers in the Northern Hemisphere to study the variations of auroral electrojets during the sawtooth event. By comparing characteristics of enhancements of nightside ionospheric westward electrojets with those of positive magnetic bays of H components in the middle/low‐latitude ground magnetic field after each sawtooth injection, it is demonstrated that there are current wedges formed during this sawtooth event. The local time width of current wedges suggested by the two observations are both around 11 hours (MLT). In addition, time durations of middle/low‐latitude magnetic bays to reach maximum variations were generally longer than those for high‐latitude electrojets, implying that source currents for middle/low‐latitude magnetic bays are multiple.

One-dimensional spherical elementary current systems and their use for determining ionospheric currents from satellite measurements

Abstract The method of 1D spherical elementary current systems (SECS) is a new way for determining ionospheric and field-aligned currents in spherical geometry from magnetic field measurements made by a low-orbit satellite. In contrast to earlier methods, the full ionospheric current distribution, including both divergence-free and curl-free horizontal currents, as well as field-aligned currents, can be determined. Placing infinitely many 2D SECSs of identical amplitudes at a constant latitude results in two types of 1D SECSs, which are independent of longitude, and by superposition can reproduce any ionospheric and field-aligned current system with the same property. One type of the 1D SECSs is divergence-free and toroidal with a poloidal magnetic field, and the other type is curl-free and poloidal. Associated with the divergence of the curl-free type are radial currents. The magnetic field of the combined curl-free 1D SECS and field-aligned currents is toroidal and restricted to the region above the ionosphere. Ionospheric currents are determined by placing several 1D SECSs at different latitudes and choosing their amplitudes in such a way that their combined magnetic field as closely as possible fits the one measured by the satellite. The 1D SECS method has been tested using both modeled and real data from the CHAMP satellite, and found to work excellently in 1D cases.

One-dimensional upward continuation of the ground magnetic field disturbance using spherical elementary current systems

Ionospheric equivalent currents are defined as spherical sheet currents, which reproduce the observed magnetic disturbances below the ionosphere. One way of determining these currents is to place several so called spherical elementary current systems (SECS) in the ionospheric height and to solve an inversion problem for the amplitudes of these systems. In previous studies this method has been applied to two-dimensional data sets, having both latitudinal and longitudinal spatial coverage (2D SECS method). In this paper a one-dimensional variant of this method (1D SECS) is developed. The 1D SECS method can be used even in those situations where the data set is one dimensional, e.g. with one meridionally aligned magnetometer chain. The applicability of the 1D SECS method is tested using both synthetic and real data. It is found that in real situations the errors in the 1D SECS results are 5—10% in current density profiles and ~5% in integrated currents, when compared to the results of the more accurate 2D SECS method.

Separation of the geomagnetic variation field on the ground into external and internal parts using the spherical elementary current system method

Traditionally the separation of the ground geomagnetic field variations into external and internal parts is carried out by applying methods using harmonic functions. However, these methods may require a separate field interpolation and extrapolation, can be computationally slow, and require a minimum wavelength to be specified to which the spatial resolution is limited globally. A novel method that utilizes elementary current systems can overcome these shortcomings. The basis is the fact that inside a domain free of current flow, the magnetic field can be continued to any selected plane in terms of equivalent currents. Two layers of equivalent currents, each composed of superposition of spherical elementary systems, are placed to reproduce the ground magnetic field: One above the surface of the Earth representing the field of ionospheric origin, and one below it representing the field caused by induced currents in the Earth. The method can be applied for single time steps and the solution of the associated underdetermined linear system is found to be fast and reliable when using singular value decomposition. The applicability of the method is evaluated using synthetic magnetic data computed from different ionospheric current models and associated image currents placed below the surface of the Earth. Following these tests, the method is applied to the measurements of Baltic Electromagnetic Array Research (BEAR) (June–July 1998). External and internal components of geomagnetic variations were computed for the entire measurement period. Also the adequacy of the sparser IMAGE magnetometer network for the full field separation was tested.

Ionospheric equivalent current distributions determined with the method of spherical elementary current systems

The ground magnetic field disturbance caused by ionospheric currents can be represented by equivalent currents placed to the ionospheric plane. Equivalent currents provide valuable information about the ionospheric electrodynamics, and thus they can be used, for example, in studies of space weather, ionosphere‐magnetosphere coupling, and the magnetotelluric source effect. We derive equivalent currents by using the spherical elementary current system method. The applicability of the method for the Baltic Electromagnetic Array Research (BEAR) magnetometer array is validated by means of synthetic ionospheric current models and by investigating the goodness of the fit between the modeled and measured ground magnetic field. The applicability of the method for the sparser International Monitor for Auroral Geomagnetic Effects (IMAGE) magnetometer network is also proved. In addition, the combination of the elementary current system method and the complex image method, used for the calculation of the induced electromagnetic fields on ground, is introduced, and the combination of the methods is tested by using geoelectric field data from the BEAR project. Our special interest is in the effects that rapidly varying ionospheric currents have on technological conductor systems at the surface of the Earth due to geomagnetically induced currents. Comparison between equivalent currents and the time derivative vector of the horizontal magnetic field emphasizes the importance of small‐scale structures.