Empirical Modeling of Ionospheric Current Using Empirical Orthogonal Function Analysis and Artificial Neural Network

Abstract

The dominant drivers of the large-scale spatial and temporal variability in the upper atmosphere are external forcing by energetic solar radiation (such as extreme ultraviolet) and energy deposition from the magnetosphere, as well as wave forcing from the lower atmosphere. The dynamo process in the E-region ionosphere brings about the solar quiet (Sq) current, which can be inferred from the so-called geomagnetic Sq variations. In the high-latitude ionosphere, the magnetospheric electric fields, which are coupled with the solar wind velocity and interplanetary magnetic field (IMF), are the primary drivers of the electric fields and currents (e.g., Weimer, 2005Weimer, , 2013, while in lower latitude regions, the neutral winds influenced by solar tides play a more active role (e.g., Maute & Richmond, 2016;Richmond & Thayer, 2000). In the equatorial region, a considerable daytime rise in the eastward equatorial electrojet (EEJ) current dominates the

Ionospheric Current Variations by Empirical Orthogonal Function Analysis: Solar Activity Dependence and Longitudinal Differences

“…Then, SHA is performed on ΔH, ΔD and ΔZ components at each geomagnetic colatitude based on dominant harmonics rank m in the range 0 ≤ m ≤ 4 to calculate the spherical harmonic coefficients. Consequently, the Sq current functions over the two longitudinal sectors were obtained for each IQD at every hour of LT and geomagnetic colatitude, respectively based on Equation (e.g., Owolabi et al., 2021; Yamazaki & Maute, 2017). $$$\begin{array}{l}J(t,\theta )=-\frac{10R}{4\pi }\sum\limits _{n=m}^{m+9}\sum\limits _{m=0}^{n}\frac{2n\hspace*{.5em}+\hspace*{.5em}1}{n\hspace*{.5em}+\hspace*{.5em}1}{(\frac{r}{R})}^{n}\left\{\begin{array}{l}{E}_{n}^{m}\hspace*{.5em}\mathrm{cos}(mt)\hfill \end{array}\right.+{e}_{n}^{m}\hspace*{.5em}\mathrm{sin}(mt)\right\}{P}_{n}^{m}(\mathrm{cos}\varphi )\hfill \end{array}\hspace*{.5em}$$$ where $$r=R$$ is assumed in the calculations because $$\vert r-R\vert \ll R$$, $${P}_{n}^{m}(\mathrm{cos}\hspace*{.5em}\varphi )$$ is the associated Legendre function of geomagnetic colatitude, $$n$$ and $$m$$ are the degree and order at which the series of harmonics function is truncated, …”

“…The morphology of the Sq current variation appears like oval‐shaped horizontal current sheet in the ionosphere, forming two oppositely oriented loops on the dayside in each hemisphere: one anticlockwise in the northern hemisphere (NH) and one clockwise in the southern hemisphere (SH), with the foci of the loops located near noon in the middle latitudes (e.g., Owolabi et al., 2021; Pedatella et al., 2011; Richmond, 1998; Yamazaki et al., 2011). At the geomagnetic equator, where ions and electrons are magnetically coupled, the electric and magnetic fields intersect, resulting in a local increase in ionospheric conductivities and a large eastward flow of equatorial electrojet (EEJ) current during the daytime (e.g., Alken & Maus, 2007).…”

“…Chen et al., 2007; Cousins et al., 2015; Shore et al., 2016). This empirical model is appropriate for geomagnetic field modeling since it decomposes the signal into uncorrelated eigenmodes, resulting in eigenfunction expansion used to probe the time‐varying Sq current (e.g., Alken et al., 2017; Owolabi et al., 2021). Different sources have been proposed for Sq current variations, including long‐term variation in geomagnetic activity (e.g., de Haro Barbas et al., 2013), solar variability (e.g., Torta et al., 2009) and the secular variation of the geomagnetic field (e.g., Cnossen & Richmond, 2013; Soares et al., 2020).…”

“…We utilized ground magnetometer data from 2006 ‐ 2019 to produce continuous observations of the Sq current function using spherical harmonic analysis (SHA) and examine its spatial as well as temporal variations under different solar activity levels over the American and European/African sectors. Subsequently, the EOF technique was used to reconstruct a two‐dimensional (2‐D) model of the Sq current under certain condition of solar flux, magnetic latitude, local time and season over the two longitudinal sectors using the dominant spatial geometries, as the EOF technique has been noticeably effective in characterizing the spatial and temporal variations (e.g., Alberti et al., 2020; Alken et al., 2017; Owolabi et al., 2021). First, we have attempted to find the similarities as well as differences in the spatial and temporal variations of the Sq current.…”

“…It was remarked that due to variations in the ionospheric conductivity and neutral winds, the Sq current system exhibits hemispheric asymmetry, with its strength in the summer hemisphere being greater than that in the winter hemisphere. A large number of studies have been devoted in understanding the seasonal and solar activity variations of the Sq current (e.g., Matsushita & Maeda, 1965;Owolabi et al, 2021;Takeda, 2002;Takeda et al, 1986). For example, Yamazaki et al (2011) found strong annual and semiannual changes of the Sq current in the northern and southern hemispheres, which Pedatella et al (2011) also found in the European/African sector during solar minimum.…”