The Response of Ionospheric Currents to External Drivers Investigated Using a Neural Network‐Based Model

A predictive model for the variation of ionospheric currents is of great scientific and practical importance to our modern industrial society. To study the response of ionospheric currents to external drivers including geomagnetic indices and solar radiation, we developed a feedforward neural network model trained on the Equivalent Ionospheric Current (EIC) data from 1st January 2007 to 31st December 2019. Due to the highly imbalanced nature of the ionospheric currents data, which means that the data of extreme events are much less than those of quiet times, we utilized different loss functions to improve the model performance. Our model demonstrates the potential to predict the active events of ionospheric currents reasonably well (e.g., EICs during substorms) within a timescale of a few minutes. Although the data used for training are measurements over the North American and Greenland sectors, our model is not only able to predict EICs within this region, but is also able to provide a promising out‐of‐sample prediction on a global scale.


Introduction
It is well known that geomagnetic field disturbances can occur at high latitudes due to the strong ionospheric electrojet currents that form during substorms and geomagnetic storms.These large magnetic disturbances, usually characterized by a sharp variation of the magnetic field, also produce geoelectric fields and Geomagnetically Induced Currents (GICs).The active GICs can flow through equipment and various facilities connected to the ground, such as subsurface pipelines, railway systems, and electrical power systems.An extreme GIC event may damage so much equipment that it can cause large-scale blackouts (Boteler, 2001(Boteler, , 2019;;Pirjola, 2000;Pulkkinen et al., 2017).The risk of GICs to equipment can be estimated if the magnetic field time series and ground conductivity are properly specified (Gil et al., 2021;Love et al., 2018;Lucas et al., 2020).Therefore, predicting the occurrence time and locations of GIC events is essential for protecting modern society.
However, GIC data is not readily accessible since it is not directly monitored and measured at all points, at all times.Previous studies attempted to investigate the magnetic field variation (dB/dt) as a proxy of GICs by utilizing, for example, numerical simulations (Tóth et al., 2014;Wintoft et al., 2015) or machine learning models (Blandin et al., 2022;Pinto et al., 2022).However, the GIC system is largely represented by variations of the ionospheric currents (Ngwira et al., 2018;Pulkkinen et al., 2015;Viljanen et al., 2001), which themselves can be derived from magnetic field perturbations measured on the ground.The Equivalent Ionospheric Currents (EICs) can be thus estimated based on the Spherical Elementary Current Systems (SECS) technique (Amm & Viljanen, 1999;Weygand et al., 2011).Therefore, understanding how EIC develops in response to external drivers such as geomagnetic indices can provide us with the key information needed to build predictive models that describe the variation of GICs.However, prediction of the EIC system using machine learning techniques has been insufficiently studied in the past.
To study the response of EIC to external drivers such as geomagnetic indices and solar radiation, we developed an Equivalent Ionospheric Currents-Spatial Temporal (EIC-ST) model.This model applies a feedforward neural network to reproduce the ionospheric current derived using the Spherical Elementary Current (SEC) technique applied to North American and Greenland (Weygand et al., 2011).The conventional statistical analysis is incapable of providing a quantitative prediction and reproduction of the EIC amplitudes with relatively high accuracy due to the high nonlinearity of this system.Compared to traditional numerical or analytical models, machine learning models provide extremely short inference time for the out-of-sample prediction once the model training is completed.The easy deployment and fast iteration of machine learning models with the accumulation of EIC data provide a powerful tool to investigate the basic physics of magnetosphere-ionosphere coupling as well as address the space weather impact of GICs.The data utilized in this work are measured by multiple spacecraft and ground-based observations from the OMNI database, and the target values of the EIC-ST model are the EICs obtained using the SEC technique, including different spatial components of the EIC.
Here, we focus on modeling the east-west component of the EICS for studying the ionospheric electrojets.The input parameters (commonly referred to as "features") include the locations of the measurements (longitude and latitude), the solar radio index F 10.7 , and geomagnetic indices (e.g., AU, AL, SYM-H).We find that our model shows promise in predicting the response of Earth's ionospheric currents to the external drivers listed above.Our model is designed to provide a spatial and temporal reconstruction of the ionospheric currents, which is particularly helpful whenever and wherever they are not directly available from the observation data.

Data Sets
In this study, we develop a neural network-based model of the eastward-westward component (Jy) of the EICs to investigate their spatiotemporal evolution and make meaningful estimates for potential usage in GIC prediction.The Jy component is closely associated with the Substorm Current Wedge (SCW) system, and is the main component in the ionosphere (Gjerloev & Hoffman, 2014).The EIC data used for building the model are derived from multiple ground-based magnetometer arrays over Canada, Greenland, and the United States (Weygand et al., 2011), by using the spherical elementary currents systems (SECS) technique (Amm & Viljanen, 1999).The original EIC currents were derived at a 10-s cadence at each virtual grid in 2007-2019, and we used a 1-min resolution in our model.Although the ground magnetometer stations are irregularly distributed, the EICs grid is spaced evenly every 6.9° longitude and 2.9° latitude over the North American and Greenland sectors (see Weygand et al., 2011 for more details), as shown in Figure 1.In addition to EICs, another product of the SECS technique is the current amplitudes, which serve as a proxy for the field-aligned currents, which are currently beyond the scope of this study and will be investigated in our future work.
The OMNI data set provides a variety of space physics parameters, including solar wind conditions and geomagnetic indices.The specific input parameters used in our model, which act as external drivers, include the solar radio index F10.7 (solar radio flux) given with a 1-hr resolution, and geomagnetic indices, for example, AL (lower envelope of the auroral electrojet indices indicating the strength of the westward electrojet), AU (upper envelope of the auroral electrojet indices indicating the strength of the eastward electrojet), SYM-H (symmetric ring current intensity index) at a 1-min resolution.To study the spatial dependence of the EIC system, the locations of virtual grids are also included in the input parameters.In the model, we did not directly utilize the geographical locations (e.g., longitude and latitude).Instead, a slightly transformed version of these parameters The virtual grid locations of EIC over the North American and Greenland sectors are distributed over the same region as the ground-based magnetometers (Weygand et al., 2011).
was used in the model to meet the normalization requirement, for example, sin(longitude), cos(longitude), sin(latitude), cos(latitude), sin(15*LT), and cos(15*LT), where LT represents local time, and 15 is the constant of conversion from LT (0-24) to the corresponding longitudes between 0 and 360°.
Figure 2 shows 11 years of the input parameters: AU, AL, AE, Sym-H, and sunspot number (Figures 2a-2d) from 2007 to March 2018 (when the auroral electrojet indices ended), and the EIC Jy variations near the midnight meridian as a function of magnetic latitude (Figure 2e) and magnetic local time (Figure 2f), which roughly covers Solar Cycle 24.The last two panels indicate how the EIC Jy varies spatially (with different magnetic latitude or magnetic local time) and temporally (with time).The color-coded current density is averaged over the time range 06:00-08:00 UT daily, when the North American and Greenland sectors were close to the midnight meridian.The intensity of Jy has been observed to be relatively low during the 2008-2010 solar cycle minimum.Please note that missing data of EIC exists over 100 days of 2009 (mostly between May and September).The enhancement of Jy was observed after 2011. Figure 2 shows a "keogram" with a restriction of longitude between ∼160°W and 90°W, and the "ewogram" with a restriction of magnetic latitude between 60° and 80° during the 24th solar cycle.Most of the related substorm events can be observed between around 60° and 80° north in magnetic latitude or between ∼50° and 70° north in geographic latitude, and can be observed in the range of −50° to −150° west between 06:00 and 08:00 UT, as the North American and Greenland sectors were present in the midnight meridian.The longterm observation shows that the enhancement frequency of ionospheric currents increases as the sunspot number increases, which appears to be consistent with the solar cycle period.
It is important to note that the EIC data is highly imbalanced because there are significantly more quiet-time intervals than magnetospheric substorms or storms.Therefore, there are more small Jy values than large values in magnitude, which means the majority of the time consists of a relatively quiet ionospheric current pattern, and the active ionospheric currents appear in the minority of the time.Such an imbalanced-type distribution pervasively exists in space physics data and many other scientific data sets.Because the regression model is apt to be dominated by the vast majority of the imbalanced data, the modeled EIC pattern during active periods is prone to be poorly learned by the model.Thus, we need to customize the objective/loss function to emphasize the minority of the data set and penalize the majority of the quiet time values since they are of relatively little interest, so that the model learns better how EIC responds to its drivers during active periods.

Model Development
In this paper, we utilize a simple, feedforward artificial neural network (ANN), which is broadly used in the physical sciences for regression and classification problems.The ANN model structure is capable of highly efficient parallel computation, with a high degree of interconnection between neurons in different layers.The multiple layers of neurons provide a high measure of generalizability that can fit the typically complicated non-linear relationships between the input parameters (or independent variables) and the outputs/targets (or the dependent variables).To model the temporal and spatial response of the ionospheric currents to the external drivers, an ANN with three hidden layers is used (see Figure 3).The number of neurons in each layer was set to be 256, 192, and 128 respectively, which was determined from trial and error experimentation.We tested different numbers of hidden layers and also tried different combinations of the node numbers for each layer, the result of which did not significantly outperform the three layers network in this EICs work.The input layer enables the network to receive the input parameters or features, and then passes their signals to the following three hidden layers, with the proper non-linear activation function.In this model, we used the Exponential Linear Unit (ELU), the equation of which is: Compared to another popular activation function, the rectified linear unit (ReLU), which has the potential issue of gradient vanishing, the ELU has the property that prevents such a problem.This is because the ELU function utilizes a non-linear negative part with a non-zero curve instead of simply setting it to be zero, as the ReLU does, which is prone to the gradient collapse issue.We also tested using other activation functions, such as ReLU or sigmoid, and found that they did not perform better than ELU in our model.To avoid potential overfitting, the model chooses to drop out 20% of neurons of each layer randomly.Such a dropout operation can enhance the generalization ability of the network (Srivastava et al., 2014).The signals passing through the hidden layers are eventually sent to the output layer of the ANN, which represents the modeled target (EIC Jy).Using the back-propagation algorithm (Rumelhart et al., 1986), the model is trained by iteratively updating its weights and biases in all active neurons.In each step during the training process, the value of the loss function is calculated for the training data set using the adaptive gradient descent algorithm, for example, NAdam (Dozat, 2016).To further reduce overfitting, at the end of each epoch of the training process, the validation loss is also monitored for the early stopping strategy.The model training process stops when the validation loss does not decrease after a certain number of epochs.The number of epochs for the early stopping strategy in our model is set to 25.More details of this model are given by Chu et al. (2017).
The input parameters in the model include AL, AU, SYM-H, and solar index F 10.7 indices from the OMNI database as well as the locations of the EIC virtual grids, as mentioned in the data set section.We used the time series of these indices, which include both instantaneous values and their time histories, to investigate the response of the east-west electrojet to the above-mentioned external drivers.This is because the preceding states of magnetospheric activity and solar radiation heavily impact the variations of the EICs.The AL and AU indices use four different temporal resolutions, which were determined empirically: 5-min averages for the preceding 1 hr; 30-min averages for the preceding time from 1 to 3 hr; 180-min averages for the preceding time from 3 hr to 1 day; and 720-min averages for the preceding time from 1 to 2 days.The SYM-H index adopts the same temporal resolutions as the AL and AU indices, except for the first resolution, being 10 min for the preceding 1 hr.The F 10.7 index is measured with a daily cadence, but OMNI provides its derived hourly values; therefore, we adopt 720 min resolution consistently for the preceding 2 days.The details of the external drivers' historic time series and resolutions are shown in Table 1.The whole data set is divided into daily segments and then randomly split into the training set (60%), the validation set (20%), and the test set (20%).The test data set has never been used during the training process and has only been utilized as a performance indicator for out-of-sample prediction.The total number of data points in the whole data set is over 1.15 × 10 9 .
Training the model with imbalanced EIC data, the mean square error (MSE) and a focal loss (L4) are utilized as loss functions to be minimized, for comparatively studying the improvement of the imbalanced regression by

Table 1
The Time History and Resolutions of AL, AU, SYM-H and F10.7 Indices different loss functions.Many other machine learning models dealt with the imbalance problem by manually selecting only extreme events to improve the performance, for example, (Hu et al., 2023;Ren et al., 2023).We avoid providing such a priori knowledge to the predictive model, such that our model is robust to provide continuous predictions/forecasts in the real operational environment.MSE is defined as the mean value of the square of the difference between every observation value and model prediction value, as Equation 2 shows.Similarly, the focal loss function is defined as Equation 3, equivalent to a weighted MSE, where the weight   = ( − ỹ) 2 .
The focal loss is used to impart more weight to the most extreme (and rare) samples which have larger errors (Lin et al., 2017).In contrast, the right four panels reveal that the focal loss model has a more variable error distribution with respect to local time, which is likely to be caused by the emphasis of the focal loss function on the more extreme-valued samples.A more detailed discussion will be given in the following event analysis section.

Event Analysis
In this section, the EIC-ST model is applied to two substorm events to demonstrate its capability to reconstruct the east-west electrojets.It is noteworthy that both events are taken from the test data set (i.e., not the training data set which is used to create the model).Therefore, the event analysis demonstrates the out-of-sample prediction ability of the model.

29th June 2015 Substorm
The EIC-ST model was applied to a moderate substorm occurring on 29th June 2015.Figure 6 shows the comparison of the EIC observation with the MSE model and focal loss model results at the enhancement time of the westward electrojet.The left panels in the figure indicate an intensive westward electrojet measured around the mid-to high-latitudes in the North American and Greenland sectors.The MSE model predicted this electrojet within the corresponding location but underestimated its magnitude, as expected.In contrast, the focal loss model reconstructed a much more consistent westward electrojet in location and magnitude, reproducing the extreme values of Jy in this event.We noted that a minor and weak eastward electrojet was measured at the pre-midnight sector in the observation, which has not been produced either in the MSE model or the focal loss model at this time.However, the focal loss model captured the eastward electrojet in the same location a few minutes before this time, consistent with the simultaneous observation, which will be shown and discussed in Figure 8.
The substorm growth phase started around 07:45 UT, when the AL index started to decrease.The measurement of geomagnetic indices AL, AU, and SYM-H are shown in Figures 7a and 7b.Panels (7c and 7d) show the keograms (time-versus-magnetic latitude) of observations and model predictions during this substorm event.The panels (7e and 7f) provide the ewograms (time-versus-magnetic longitude) of observations and model predictions.To better cover the auroral zone and westward electrojet, the keograms are calculated within the longitudes between ∼160°W and 90°W, by averaging the values at the grids in specific magnetic latitude ranges.Similarly, the ewograms are calculated using the mean values along longitudes between the magnetic latitude of 60° and 80°.
The onset of the substorm expansion phase started around 08:30 UT, with a local enhancement of the westward electrojet between around 60° and 75° magnetic latitudes, as the third panel in Figure 7 shows.The intensity of  The comparison between observation and model predictions for the two models reveals that the time of substorm onset and the magnetic latitude location of the westward electrojet have both been correctly captured (around 8:30 UT, between ∼65° and 75°N).Specifically, during the substorm expansion process, the SCW connected with the ionospheric current was expected to expand longitudinally with time (Lopez, 1990), which has also been well captured by our model, as the ewograms (Figures 7e and 7f) show.Comparing the prediction results made by the models with MSE and focal loss methods, the results show that the focal loss emphasizes the magnitude of the extreme values of the westward electrojet during the substorm and better predicts its minimum value.In contrast, the EIC Jy during the substorm appears to be underestimated by the MSE model method, since the associated large ionospheric currents fall into the minority of the data set.Similarly, the ewogram of the focal loss model demonstrates a better consistency with observations compared to that of the MSE model.In general, we found that the focal loss model more accurately reproduces the observations than the MSE model.

29th February 2008 Substorm
Figure 8 shows another event analysis for a stronger substorm occurring on 29th February 2008.The AL index gradually decreases starting from 07:45 UT (Figure 8a), and at about 08:20 UT, the SYM-H index increases (Figure 8b), shown in the same format as Figure 7.An interesting feature of this substorm is that there were two distinct enhancements in the westward electrojet around 08:32 UT and 09:02 UT, respectively, as shown in the AL index, the keogram (Figure 8c), and ewogram (Figure 8e).Multiple enhancements in the westward electrojet of the SCW are generally believed to be caused by sequential earthward flows.Our EIC-ST models successfully predicted onsets and locations of the multiple electrojet enhancements, as shown in the modeled keogram (Figure 8d) and ewogram (Figure 8f).In addition, the magnetic longitudinal and latitudinal expansion of the westward electrojet was also well captured by our models.The predicted onset time is consistent with the observations.The magnetic latitude of the westward electrojet predicted by the model is between ∼65° and 75°N, corresponding with the observation.The last panel shows the mean values of observed and predicted EIC Jy.The MSE model underestimated the observations compared to the focal loss model, which more closely matched the timing and magnitude.Therefore, our results indicate that the focal loss model outperforms the MSE model.The predictions made by the focal loss model matched the current magnitude of the observations and the substorm expansion time.

Global Prediction
In addition to the out-of-sample prediction of the time series demonstrated above, our model also provides the prediction ability for the out-of-sample spatial locations.The spatial coverage of the EIC training data is limited in the North American and Greenland region.A global observation is needed but does not exist.However, the EIC-ST model could be utilized to reconstruct the global distribution of the EIC Jy. Figure 9 shows a series of reconstructions in the northern hemisphere (35°N-85°N) across all longitudes (180°W-180°E).The four time snapshots were taken during the substorm event on 29th June 2015: (a) 07:50:00 UT, (b) 08:35:00 UT, (c) 08:50:00 UT, and (d) 09:15:00 UT.In each snapshot, the lower panel shows the predicted contour map in spherical geographical coordinates from the north-pole perspective.The upper panel shows the same prediction in the rectangular geographical map, and the middle panel reveals the observation map at the same timestamp.The first time snapshot was near a quiet time before the substorm onset.The current pattern in the mid-latitudes and high-latitudes is fairly weak and localized.Soon after the substorm onset, Figure 9b shows that the westward currents started to enhance between magnetic latitudes 60° and 80°, which is consistent with observations.The westward electrojet crossed the longitudes from pre-to post-midnight regions, where the simultaneous eastward current was attached near the duskside at the lower latitude.The relative slip between westward and eastward currents might be related to the Harang discontinuity, a full examination of which is beyond the scope of the present study.The predicted amplitude of the westward electrojet matched the observation reasonably well.Figure 9c (top) shows the snapshot at the peak amplitude of the observed westward current, showing that the electrojet roughly remained at its location.The predicted electrojet current was expanded to a more global scale such that a wider longitude range was covered.During the recovery phase, the currents gradually diminished, as shown in Figure 9d.
Based on this global prediction result, the westward electrojet locations on a global scale are consistent with magnetic latitudes within a specific range, which is supposed to be associated with the polar region linking with the SCW.In addition, an eastward ionospheric current was predicted near the pre-midnight sector, located at relatively lower latitudes compared to the westward electrojet.The eastward electrojet is likely the ionospheric segment of the Partial Ring Current (PRC).The existence of the PRC has been discussed in a number of studies, including observational and modeling efforts (Grafe & Feldstein, 2000).However, due to the longitudinal limitation of the grid locations, it is difficult to estimate its approximate longitudinal and latitudinal location and its extension.Our model provides a reasonable prediction for the PRC and shows that the PRC extends from pre-midnight to noon meridian.Our model provides a potential tool to study the relative strength of the eastward electrojet compared to the westward electrojet.

Long-Term Prediction
In this section, we demonstrate the long-term prediction of the model over almost 12 years.Figure 10 shows the AU, AL, and SYM-H indices during this period, and the comparison of keograms and ewograms between the observations and model predictions in the lower four panels.The model prediction of the EIC shows a consistency between the eastward-westward electrojets and the magnetospheric indices.When significant perturbations of the magnetospheric indices occur, the electrojets usually appear in the keogram and ewogram, similar to the observations.The predictions show that our model has a reasonably good ability to predict the locations and occurrence time of the related electrojets.Corresponding to Figure 2, the keogram and ewogram produced by our model show a consistent variation of EIC Jy with the observation.In such a long term, the predicted intense and weak activities match the corresponding period of solar maximum and minimum.Meanwhile, it is noteworthy that the long-term prediction is not perfectly identical to the observation, likely because of EIC data's imbalanced nature.

Conclusions
To predict the response of EIC to magnetospheric indices and solar radio fluxes, we have developed a feedforward neural network trained on EIC data collected over the North American and Greenland sectors.We found that the time series of these indices provides good indicators to predict the variations of EIC along the eastward-westward direction.We note that the EIC data is highly imbalanced, which means the majority of the data occur during quiet times that are of little interest, and the active times we are more focused on for studying the magnetospheric events such as substorms represent the minor portion of the data set.To overcome this imbalance issue, we utilized two different loss functions, MSE and focal loss, to investigate how different loss functions affect the model prediction results, where the latter penalizes model mismatch at the more extreme data values.Based on a comparison of the model results, we found that the focal loss model method improves the regression performance for the imbalanced EIC data.The advantage of focal loss is that this method keeps the original data distribution.Our model is not only able to predict the out-of-sample events along the time series, but is also able to provide the out-of-sample predictions beyond the observation locations such that the estimation for the regions without observations becomes possible, although the performance of such an estimation needs to be further studied.We conclude that our model provides a promising prediction tool for the spatial and temporal variation of the EIC system with a rapid inference ability.

•
A neural network is trained to predict the response of Equivalent Ionospheric Currents (EIC) to geomagnetic indices • A comparative study between the mean square error and focal loss has been made to address the EIC's imbalance regression problem • Our model can spatially and temporally predict the eastward-westward EIC component

Figure 1 .
Figure1.The virtual grid locations of EIC over the North American and Greenland sectors are distributed over the same region as the ground-based magnetometers(Weygand et al., 2011).

Figure 2 .
Figure 2. The Sunspot Number, Sym-H, AE, AU, and AL in panels (a)-(d) as indicated in the insets, during the 24th solar cycle, with the simultaneous long-term EIC Jy's keogram and ewogram in panels (e) and (f).The red color represents westward EIC, and blue represents eastward EIC in the keogram and ewogram.

Figure 3 .
Figure 3.The model architecture of ANNs.From bottom to top, the input layer, the three hidden layers, and the output layer are displayed.The neurons in each layer are interconnected to pass the input signals through the network to the output neuron.

Figure 4
Figure4shows the correlation between the observed and modeled EIC Jy for the whole, training, validation, and test data sets, respectively.The color bar displays the number density of observation-prediction samples on a logarithmic scale.The diagonal red dashed line in each panel represents the ideal agreement (y = x) between observed and predicted values.There is a high concentration of number density within the range of low observation values near the diagonal area, which demonstrates that the majority of observational data is dominated by the quiet EIC pattern.The samples with relatively low density are scattered around the diagonal, and most of the values fall into the area closer to the diagonal.This histogram indicates that those values are reasonably estimated by the model.The left panels show the model performance with the MSE loss function (hereafter, MSE model), which is dominated by the small values.The prediction of large samples is thus highly underestimated.In contrast, the model with a focal loss (hereafter, focal loss model) (right four panels) places more weight on the

Figure 4 .
Figure 4. Correlation between the ground-based observation of the EIC Jy and the artificial neural network modeled values for all, training, validation, and test data sets, respectively.The left four panels are the model results produced by mean square error (MSE), and the right four panels are those produced by focal loss results.The color bar represents the number of observation-prediction samples on a logarithmic scale.The diagonal red dashed line indicates perfect agreement between observation and prediction, that is, where y = x.The correlation coefficient r and root MSE are also shown in each panel.

Figure 5
Figure 5 shows the error distributions as a function of the local time for the whole, training, validation, and testing data sets, comparing the MSE and focal model performance.The MSE model appears to have a relatively evenly distributed error bar and mean values with respect to local time, as the left four panels show.In contrast, the right four panels reveal that the focal loss model has a more variable error distribution with respect to local time, which is likely to be caused by the emphasis of the focal loss function on the more extreme-valued samples.A more detailed discussion will be given in the following event analysis section.

Figure 5 .
Figure 5.The error between the observation and model predictions, as a function of local time, for all data, training, validation, and test data sets, respectively.The black symbols represent the mean values of the error, and the red error bars represent the standard deviation of the error.

Figure 6 .
Figure 6.Snapshots of the observed (left panel) and predicted (center and right panels) westward electrojets during the 29th June 2015 substorm event.Both the mean square error model and focal loss model results are shown in geographic coordinates.The red color represents the westward current, and the blue represents the eastward current.The solid black line represents the midnight line, and the solid purple line represents the dawn-dusk line.
the westward electrojet increased to the maximum values around 08:50-08:55 UT, which is clearly shown in the keogram and ewogram of the observation.The last panel displays the mean value of westward EIC Jy over the grids of the ionospheric currents measurement.

Figure 8 .
Figure 8.The observation and model predictions of EIC Jy for the 29th February 2008 substorm.In the left column are the results associated with the mean square error model, and in the right column are the results associated with the Focal Loss model.The first two panels display the geomagnetic indices AU, AL, and SYM-H between 07:30 and 10:00 UT.The third and fourth panels show the keograms (time-versus-magnetic latitude) of observations and model predictions during this substorm event.The fifth and sixth panels provide the ewogram (time-versus-magnetic longitude) of observations and model predictions during this substorm event.The color represents the intensity of the EIC Jy, where the positive (blue) indicates eastward ionospheric current and the negative (red) indicates westward ionospheric current.The last panel shows the mean value of westward EIC Jy over all grid locations of the ionospheric currents measurement, where the red curve represents the observation values, and the blue curve represents the model predictions.

Figure 9 .
Figure 9.Comparison between the model global prediction across all longitudes (upper panels) and the observation of EIC Jy within North America and the Greenland sector (middle panels).The north pole view of predicted EIC Jy in the spheric coordinate is also presented on the lower panels.The color represents the amplitude of the westward-eastward electrojet current.In the upper and middle panels, the dashed lines represent magnetic longitudes and latitudes, and the solid vertical line indicates the midnight line.In the lower panel, the solid purple line represents the dawn-dusk terminator, and the black and blue solid lines represent the midnight and noon lines at the specific universal time, as shown in the figure.