Modeling of Topside Ionosphere and Plasmasphere

We developed a new topside ionosphere and plasmasphere model using a machine learning technique using approximately ve million electron density datasets from the Japanese satellites, namely, Hinotori, Akebono, and Arase. The topside ionosphere and plasmasphere model (TIP-model) can estimate electron densities at altitudes ranging from 500 km to 30,000 km in terms of latitude, longitude, universal time, season, and solar and magnetic activities with time history. The model shows the time-dependent 3D structure of the plasmasphere in response to solar and magnetic activities. The constructed TIP-model reproduces plasmapause, plasma tail/erosion of the plasmasphere, and the plasma escape near the magnetic pole. The total electron content (TEC) in the plasmasphere was also obtained through the integration of electron density from 2,000 km to 30,000 km altitudes. The TEC of the plasmasphere is approximately 5 TECU near the magnetic equator, and it depends strongly on geomagnetic latitude, longitude, local time, and solar and magnetic activities.


Introduction
The plasmasphere is an inner part of the Earth's magnetosphere. Dense and cold plasmas (a few eV) are generated in the Earth's ionosphere. Electrons in the ionosphere move along the Earth's magnetic eld lines and those with energies larger than the escape energy can reach the inner magnetosphere; however, because ions are heavier, they cannot move to the inner magnetosphere. Therefore, an electric eld develops in the region between the ionosphere and the inner magnetosphere. The ionospheric ions begin to move upward because of the generated electric eld. The ionospheric electrons and ions move to the inner magnetosphere together. Light ions such as H + , He + , and O + can easily escape from the ionosphere.
During some hours and days, the escaping plasma accumulates until an equilibrium state is reached. The plasmasphere nearly rotates with the Earth. The region of the plasmasphere changes in size because of the geomagnetic activity, which causes a substantial loss of the plasmaspheric plasma and/or the re lling of the plasmasphere to occur during the geomagnetic active periods.
Whistler radio waves produced by lightning propagate along the Earth's magnetic eld lines through the ionosphere, plasmasphere, and magnetosphere. The radio waves change frequencies during the propagation. Carpenter (1966) observed a sharp drop in frequency dispersion at approximately 3 Re, which is the plasmapause. The imager for magnetopause-to-aurora global exploration (IMAGE) satellite observed the resonance scattering of sunlight by He + in the plasmasphere and captured images of the plasmasphere (Burch, 2000;Sandel et al., 2000). A tail on the plasmasphere, caused by plasmaspheric rotation and the electric elds generated by solar wind and magnetosphere interaction (Nishida, 1966), was also observed by the IMAGE satellite. The IMAGE satellite also showed the occurrence of interesting phenomena such as ngers, crenulations, channels, notches, shoulder, and shadow.
The plasma density gradient in the radial direction at the equator was estimated using ULF wave observations on the ground and satellite observations (Angerami and Carpenter, 1966;Denton et al., 2009; Sandhu et al., 2016). The plasma density gradient was estimated at 4-6 using the power-law model.
Plasmasphere models can either be based on satellite or ground-based observation data or are physical models. Carpenter and Anderson (1992) developed an empirical model of equatorial electron density in the range 2.25 < L < 8 using sweep frequency receiver radio measurements obtained by the international Sun-Earth explorer (ISEE) 1 satellite. The model shows the structures of the plasmasphere, plasmapause, and plasma trough for solar cycle variation. O'Brien and Moldwin (2003) developed an empirical model of the plasmapause location as a function of Kp, AE, and Dst using the combined release and radiation effects satellite (CRRES) observations. The global core plasma model (GCPM) is based on data from the dynamics explorer (DE) and ISEE satellites (Gallagher, 2000). The GCPM provides empirically derived plasma densities and ion compositions of H + , He + , and O + as functions of geomagnetic and solar conditions. The GCPM also includes models for the plasmapause, trough, and polar cap. Plasma parameters below 2,000 km altitudes were calculated using the international reference ionosphere (IRI) (Bilitza et al., 2011). An electron temperature model at 1000-10,000 km altitudes was developed based on Akebono satellite measurements (Kutiev et al., 2004). The electron densities obtained from the upper hybrid resonance (UHR) frequency measured by the plasma wave and sounder (PWS) on the Akebono satellite were tted to eld-aligned electron density pro les using the sum of exponential and power-law   Figure 1 shows the electron density as a function of altitude. Green, blue, and red dots show the electron densities from the Arase, Akebono, and Hinotori satellites, respectively. Two different distributions were observed with different electron density gradients for altitude. The upper and lower parts of the electron density distribution with respect to altitude show densities inside and outside of the plasmasphere, respectively. The upper and lower parts of the electron density distributions are also plotted in the bottom two panels. These electron density datasets include the structures of the topside ionosphere, plasmasphere, plasmapause, and plasma tail. We used the electron density datasets to construct a topside ionosphere and plasmasphere model using machine learning (TIP-model).

Topside Ionosphere And Plasmasphere Model (tip-model)
Many structures such as equatorial density anomaly, plasma trough, plasma heating/out ow in the polar region, plasmapause, plasma tail, plasma erosion, plasma re lling, and so on are in the topside ionosphere and plasmasphere, and these phenomena are strongly dependent on geographic/geomagnetic latitude and longitude, local time and season, and solar and magnetic activities. The time history effects of the plasmasphere are important for building the plasmasphere model because the plasma re lling takes a few days to achieve the plasma density along a magnetic ux tube. Because the three satellites do not cover the whole plasmasphere in time and space, approximately ve million electron density datasets from the three Japanese satellites are still insu cient to construct an empirical model of a time-dependent 3D ionosphere and plasmasphere.
A neural network combined with machine learning is a powerful technique for data modeling. We applied the neural network as a satellite in situ data interpolation method for building a time-dependent 3D topside ionosphere and plasmasphere model. The neural network model is shown in Figure 2. This model is a simple supervised model consisting of an input layer, nine hidden layers with 9216 nodes, and an output layer. The input parameters are universal time from January 1 (UT), geographic latitude and longitude, altitude, and 5 days solar ux (F10.7) and magnetic activity (Ap) indices. The output is electron density. Approximately ve million datasets were divided into 1000 groups. The TIP-model, using machine learning, learns the data of each group repeatedly. Gaussian random noise with a 1% standard deviation was added to each dataset during the learning process. The method involving learning 1000 groups repeatedly and adding Gaussian random noise was useful in avoiding over tting, which is a serious problem in building a plasmasphere model from the limited in situ satellite data. Of the approximately ve million datasets, 0.017% of the datasets, which were not used for learning, were used as test datasets to validate the learning results. Figure 3 shows the comparison between the observed electron densities of the test data and the predicted electron densities obtained by the TIP-model. Red, blue and green dots indicate the observed/predicted electron densities from the Hinotori, Akebono, and Arase satellites, respectively. The standard deviation of the difference between the observed and the predicted data is 0.17 in the topside ionosphere, plasmasphere, and magnetosphere. The TIP-model constructs the plasmasphere using the median value of the inferred electron densities from the ve training results. Figure 4 shows the predicted electron density distributions in the plasmasphere on 146.38 total day in 2017. Figure 4 (a) shows the electron densities in the geographic meridian plane. Horizontal and vertical axes indicate day-night (dayside on the right) and north-south (northern pole on the top) directions, respectively. Figure 4 (c) shows the electron densities in the geographic equatorial plane in the altitude range of 500 km to 5 Re with day-night in the horizontal (dayside on the right) and dawn-dusk in the vertical (dusk on the top) directions, respectively. The electron density gradient in the radial direction was calculated using Where n is the electron density, Ris the radial distance, and L is the characteristic electron density gradient length (km). Absolute value of the electron density gradients in the radial direction in the geographic meridional plane are shown in Figure 4  Because the magnetic activity was low for a few days, the plasmapause was outside of the satellite apogee. The electron density gradient associated with the plasmapause is not shown in Figure 4 (d). The density gradient increase before the morning may be a part of the plasmapause. The plasmasphere has day-night and dawn-dusk asymmetries in terms of the electron density distribution (see Figure 4 (b)). The TEC of the plasmasphere shows geomagnetic latitude and longitude and local time dependences. The TEC of the plasmasphere is high during the daytime of the low latitude region, with approximately 6 TECU on the magnetic equator. This value is approximately 10% or more of the TEC on the ground, which is obtained from the global navigation satellite system (GNSS).

Results And Discussions
On 147.12 total day in 2017, the magnetic activity increased and the Ap index reached 106. However, the solar activity did not change. F10.7 was 81. The plasmapause was clearly shown around 3 Re with the electron density decreasing from approximately 1,000 cm -3 (see Figure 5). The plasmapause moved to approximately 3 Re and the plasma's escape to the magnetosphere occurred in the afternoon region. The electron density increased and the escape was also observed near the northern and southern magnetic poles (see Figure 5 (a) and (b)). The characteristic density gradient of plasmapause was less than 2000 km. The TEC of the plasmasphere increased to seven TECU near the equator in the dayside.
After 147.88 total day of magnetic activity increase, the small plasmasphere was still seen (Figure 6). The small plasmasphere continued for a couple of days after the magnetic activity increased. The tail of the plasmasphere moved from afternoon to evening because of corotation of the plasmasphere. The TEC of the plasmasphere was approximately 3 TECU near the magnetic equator on the dayside. On 149.00 total day, two days after the magnetic activity increase, a clear plasmapause was generated again (see Figure  7) because of the magnetic activity increase. Therefore, it is suggested that the generation of plasmapause depends strongly on both magnetic activity and the time history.
The IMAGE satellite found small-scale structures near the plasmapause such as ngers, crenulations, channels, notches, shoulder, and shadow (Sandel et al., 2000). Because the TIP-model reproduces the average electron density distribution of plasmasphere, it cannot predict small-scale density structures. However, the accuracy of the TIP-model depends on the number of observed datasets. The use of a large number of in situ satellite data will enable the TIP-model to reproduce small-scale density structures. The TIP-model is the rst to predict the time-dependent 3D electron density distribution of the plasmasphere based on the satellite in situ observation data. The TIP-model uses 5 days Ap and F10.7 indexes because of the time history of the plasmasphere. This is important for constructing the plasmasphere response to the magnetic activity. The TIP-model estimated the TEC in the plasmasphere for the rst time. The TEC of the plasmasphere shows the magnetic latitude and longitude and local time dependences. The maximum TEC is near the magnetic equator on the dayside, and the TEC decreases during/after the geomagnetic active periods. The decrease continues for two to three days. We suggest that the TEC of the plasmasphere cannot be ignored for positioning using the GNSS.

Summary
Approximately ve million electron density datasets measured by the Hinotori, Akebono, and Arase satellites were used to develop a time-dependent 3D topside ionosphere and plasmasphere model (TIPmodel) using a machine learning technique for the rst time. The TIP-model predicts the electron densities at altitudes ranging from 500 km to 30,000 km as a function of universal time from January 1, geographic latitude/longitude, and solar and magnetic activities with ve-day histories. The TIP-model reproduces plasmapause, plasma tail/erosion of the plasmasphere, and plasma escape near the magnetic pole. The structure of the plasmasphere is strongly dependent on magnetic activity. The plasmapause moves to approximately 3 Re, and the plasma escape to the magnetosphere occurs in the afternoon region during the magnetic active period. The electron density enhancement and the escape occur near the northern and southern magnetic poles. The characteristic density gradient of the plasmapause is less than 2000 km. The TEC of the plasmasphere integrates the electron densities from 2,000 km to 30,000 km altitudes, it is ~5 TECU near the magnetic equator, and contributes to some extent to the TEC on the ground. The TEC depends strongly on the geomagnetic latitude, longitude, local time, and solar and magnetic activities.

Declarations
Availability of data and materials Data of the ERG (Arase) satellite is obtained from the ERG Science Center operated by ISAS/JAXA and ISEE/Nagoya University (http://ergsc.isee.nagoya-u.ac.jp).     Comparison between satellite observations and the predicted electron densities by the TIP-model. Of the approximately ve million datasets, 0.017 % of the datasets, were used as test datasets to validate the learning results. Red, blue and green marks indicate the observed/predicted electron densities by the Hinotori, Akebono, and Arase satellites, respectively. The standard deviation of the difference between the observed and the predicted data was 0.17 in the topside ionosphere, plasmasphere, and magnetosphere.

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