Improvement of IRI Global TEC Maps by Deep Learning Based on Conditional Generative Adversarial Networks

In this study, we make a model, which is called DeepIRI, to generate improved International Reference Ionosphere (IRI) total electron content (TEC) maps by deep learning based on conditional Generative Adversarial Networks. For this we consider 48,901 pairs of IRI TEC maps and International Global Navigation Satellite Systems (GNSS) Service (IGS) TEC maps from 2001 to 2011 for training the model. We evaluate the model by comparing IGS TEC maps and DeepIRI TEC ones from 2013 to 2017. The DeepIRI TEC maps that our model generated are much more consistent with the corresponding IGS TEC maps than the IRI TEC ones. Especially, ionospheric peak structures are successfully generated in DeepIRI TEC maps while they are not in IRI‐2016 ones. From the average differences between IRI and IGS TEC maps, our model greatly improved the IRI TEC at low‐latitude region around the equatorial anomaly. These results show that our model can improve the global TEC prediction ability of the IRI‐2016. Our study suggests a sufficient possibility to generate DeepIRI global TEC maps in near real time if IRI is generated in time. Our approach can be applied to make improved versions of empirical models if more realistic observations are available with a time delay.


Introduction
The International Reference Ionosphere (IRI) is one of the most widely used standard models of the ionosphere. It is a data-driven empirical model based on the worldwide network of ionosondes, the incoherent scatter radars, other sounders, and in situ instruments on several satellite and rockets. The IRI is an international joint project of the Committee on Space Research and the International Union of Radio Science. The IRI provides the total electron content (TEC) for a given location, time, and date as well as electron density, electron temperature, and ion composition in the altitude range from about 50 to 2,000 km (Bilitza et al., 2014;Bilitza & Reinisch, 2008).
The IRI TEC is very important to study the ionospheric behavior. In particular, the global TEC map from IRI is needed to understand the global distribution of TEC because it is impossible to measure TEC in all global regions using Global Positioning System (GPS) from the International Global Navigation Satellite Systems (GNSS) Service (IGS) stations (Kumar et al., 2015). A number of studies have evaluated how the IRI predicts the ionospheric TEC (e.g., Bilitza, 1998;Bhuyan & Borah, 2007;Coïsson et al., 2008;Jee et al., 2005;Ji et al., 2016;Kumar et al., 2015;Olwendo et al., 2013). Several studies have shown that global TEC predicted by the IRI often deviates from observation data to a rather large degree. For example, Wang et al. (2017) compared the global TEC from GPS and IRI-2012 in the spring of 2006. They found that IRI TEC agrees with GPS TEC at high latitudes and for the period from evening to morning at low latitudes. However, there are noticeable differences between them for daytime at low latitudes. Shi et al. (2019) also reported the comparison of TEC predictions by the IRI-2016 and IGS TEC maps from 2000 to 2017. They showed that there is a good consistency during low solar activity, but the IRI-2016 extremely underestimates TEC during high solar activity. Rao et al. (2019) compared the TEC from GPS and IRI-2016 during Solar Cycle 24. They found that the IRI model overestimates the noontime TEC values at low latitude.
Deep learning is a part of machine learning method based on artificial neural networks (LeCun et al., 2015). It automatically combines the feature extraction and learning together through deep network structures (Chen et al., 2019). LeCun et al. (1998) proposed the Convolutional Neural Network, which is the most popular algorithms for deep learning in the field of image processing. The Convolutional Neural Network learns directly from data and classifies images using features and patterns of the images. Goodfellow et al. (2014) proposed a deep learning method based on Generative Adversarial Networks (GANs). GANs learn a loss that tries to classify if the output image is real or fake. Isola et al. (2017) applied GANs in the conditional setting. They proposed conditional Generative Adversarial Networks (cGANs) as a general purpose solution to resolve image-to-image translation problems. These networks learn the mapping from input image to output image by applying a loss function designed to the minimization between input and output. They released the pix2pix software, a Pytorch version of their method. Using the pix2pix, Kim et al. (2019) generated farside solar magnetograms from STERO/Extreme Ultraviolet Imager 304-Å images. Their model made it possible to monitor the temporal evolution of magnetic fields from farside to the frontside of the Sun. Park et al. (2019) applied the pix2pix software to the image-to-image translation from solar magnetograms to solar ultraviolet and extreme ultraviolet images.
As mentioned above, the IRI is able to predict the global TEC map for a given location, time, and date, but the global TEC map predicted by IRI differs from observed data for some cases. In this study, we make a model, which is called DeepIRI, to generate improved IRI TEC maps by pix2pix that is a deep learning method based on cGANs. For this we consider pairs of IRI TEC maps and IGS TEC maps for training the model. The purpose of our study is to improve the IRI TEC maps by deep learning.

Data
For the global TEC of IRI, we utilize the IRI-2016, which is the latest version whose source code is available (http://www.irimodel.org/). IRI-2016 includes two new models for the F2 peak electron density height, hmF2, and a better representation of the ion composition at low and high solar activities. In addition, a number of changes were made regarding the use of solar indices and the speedup of the computer program (Bilitza et al., 2017). For the calculation of TEC, we use the CCIR option for foF2 and NeQuick topside model. We utilized the new ig_rz.dat file updated in July 2018 for the 12-month running median of the ionospheric index IG12 and solar sunspot number Rz12 (Bilitza, 2000). The IRI TECs for the global TEC maps are calculated to be the same as the resolution of IGS TEC grid which are 2 hr, 5°, and 2.5°in time, longitude, and latitude in the geographic coordinate system, respectively.
The IGS working group was created in 1998 (Hernández-Pajares et al., 2009). Since then, the four IGS Ionosphere Associate Analysis Centers, which are the Jet Propulsion Laboratory, the Center for Orbit Determination in Europe, the European Space Operations Center of the European Space Agency, and the Universitat Politècnica de Catalunya, have been continuously contributing to reliable global TEC maps. For this study, we use the IGS final vertical TEC maps (hereafter called IGS TEC map), which are more stable, reliable, and accurate (Li et al., 2018). The IGS TEC maps are obtained from the National Aeronautics and Space Administration Crustal Dynamics Data Information System (ftp://cddis.nasa.gov/ gnss/products/ionex/).
We use the global TEC maps from 2001 to 2017 for training, validation, and test data sets of the model. The data range almost covers completing solar cycle. For the purpose of training, validation, and test of the model, the data from 2001 to 2017 are divided into three sets as follows: (1) a training data set (2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011), (2) a validation data set (2012), and (3) a test data set (2013)(2014)(2015)(2016)(2017). We make 75,192 pairs of IRI TEC map and IGS TEC map. We select 48,901 pairs for the training data set, 4,389 pairs for the validation data set, and 21,902 pairs for the test data set.

Method
We adopt a pix2pix software of Isola et al. (2017) who suggested a way to resolve image-to-image translation problems. The pix2pix requires a pair of images in which input and output are related. It transforms one 10.1029/2019SW002411

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input image into the other output image by training a number of pairs of images. cGAN consists of Generator (G) and Discriminator (D) networks. The purpose of the generator is to generate plausible "fake image" to deceive the discriminator. The purpose of the discriminator is to distinguish between "fake image" generated by the generator and "real image." By learning the generator and the discriminator together, one can get a generator which generates a "fake image" that is indistinguishable from the "real image." The network structure of the generator of the pix2pix used "U-Net" (Ronneberger et al., 2015). The

10.1029/2019SW002411
Space Weather pix2pix uses a loss function in the form of cGAN, which uses an input image and random noise vector (z). The loss function of cGAN can be expressed as follows: where G is the generator, D is the discriminator, and x, y, and G(x) are the real input image, real output image, and fake output image, respectively. G tries to minimize the L cGAN loss function against an adversarial D that tries to maximize it. In addition to L1 loss, the final loss is calculated as follows: where λ is the relative weight of loss function. L1 contributes to minimizing the difference between "real image" and generated "fake image," and L cGAN contributes to generate realistic "fake image." In this study, we take this model for the image translation of IGS global TEC maps from IRI global TEC maps. Figure 1 shows the structure of our model. The process of structure is based on competition in that the generator and the discriminator have adversarial objectives to each other. In our model, the generator generates cGAN-generated TEC maps (hereafter called DeepIRI TEC maps) using the corresponding IRI TEC maps. For the first input, since the generator is not yet trained but initialized with random weight values, the generator produces an Additive White Gaussian Noise-like image. The output images of the generator become higher quality ones as the training epoch of the generator increases. DeepIRI TEC map and IRI TEC map pairs (fake pair) and IGS TEC map and IRI TEC pairs (real pair) are sent to the discriminator. The discriminator distinguishes the real pair from fake pair, and then it outputs a percentage value between 0 (fake pair) and 1 (real pair). The final layer of discriminator is a sigmoid function

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which compresses the range of input value to be in the range of [0, 1] in a continuous scale. Since the discriminator is trained to yield 0 and 1 for a fake pair and a real pair, respectively, the output of the discriminator indicates the level of reality for an input image pair. The model calculates L cGAN based on the output and then transfers L cGAN to the generator and the discriminator. The model also calculates L1 between the IGS global TEC map and the DeepIRI TEC map then transfers the value of L1 to the generator. The discriminator is trained to maximize L cGAN , and the generator is trained to minimize both L1 and L cGAN . Through this training, the model generates a DeepIRI TEC map until the discriminator does not distinguish between real pairs and fake ones. For the evaluation of model, we compare the IGS TEC maps with DeepIRI TEC maps generated using IRI TEC maps.
We train our model with 100,000 iterations, and we save the generator in every 10,000 iterations. Through this training, we acquire 10 generator networks. We compare the IGS TEC maps with DeepIRI TEC maps generated by our model using the validation data set, and then we select the best model among 10 generators.

Results and Discussions
We evaluate how well our model generates the DeepIRI TEC map. Figure 2 shows a good example of DeepIRI TEC map generated by our model. This figure shows the IRI TEC map as the input data, DeepIRI TEC map, IGS TEC map, and the difference between the last two maps at 10 UT on 26 August 2013. At this time, Kp index is 1, which is quiet time. As shown in Figure 2, the DeepIRI TEC map that our model generated is well consistent with the IGS TEC map. Especially, ionospheric peak structures in both maps are successfully generated while they are not in IRI-maps. Since sufficient and regular observations of ionosonde are not available, the IRI model predictions are not very precise at low latitude and equatorial ionization anomaly region. In addition, IRI model does not include O/N2 ration, neutral winds, and equatorial electrojet as the input parameters (Rao et al., 2019). In the difference map, we can see that the difference between DeepIRI TEC map and IGS TEC map is close to 0 TECU around ionospheric peak regions. This means that our model generates the ionospheric peak structure almost exactly like the IGS TEC map. The difference between the two maps in other regions is mostly less than 10 TECU. The correlation coefficient (CC) and root-mean-square error (RMSE) between the DeepIRI TEC map and the IGS TEC map are 0.99 and 5.7 TECU, respectively. The CC and RMSE between the IRI TEC map and the IGS TEC map are 0.96 and 12.6 TECU, respectively. The results suggest that our model greatly improves the global TEC maps, which are very consistent with the corresponding IGS TEC maps.   Figure 3 shows a bad example of DeepIRI TEC map generated by our model. This figure shows the IRI TEC map, DeepIRI TEC map, IGS TEC map, and the difference at 10 UT on 17 March 2015. At this time, Kp index is 5, which is disturbed time. As seen in the figure, although our model does not completely generate the ionospheric peak structures, our model generates the improved TEC map rather than the IRI TEC map. The CC and RMSE between the DeepIRI TEC map and the IGS TEC map are 0.9 and 19.3 TECU, while the CC and RMSE between the IRI TEC map and the IGS TEC map are 0.79 and 27.9 TECU, respectively. The large difference between the DeepIRI TEC map and IGS TEC map seems to be caused by large TEC values during the disturbed time. At this time, it is noted that the IRI model predicts the TEC to be very small. In addition, the number of TEC maps during disturbed times (Kp > 4) is relatively small than the TEC maps during quite times (Kp < 2) in the training data. This fact implies that it is difficult to successfully generate global TEC maps during disturbed time. Figure 4 shows the average differences between IRI and IGS TEC maps (top) and between DeepIRI and IGS TEC maps (bottom) for 21,902 test data. As seen in the top panel of the figure, the difference between IRI and IGS TEC maps is noticeable, especially at low-latitude region around the equatorial anomaly. Besides limited coverage of operative ionosondes and selective input uses in IRI simulation, IRI model TEC values may also deviate because it does not consider plasmaspheric contribution (Coïsson et al., 2008). But the difference between DeepIRI and IGS TEC maps is mostly close to 0. In particular, our model generates global TEC maps almost identical to IGS TEC ones including the equatorial anomaly. The comparison of two figures demonstrates that our model greatly improves the IRI TEC maps. Figure 5 shows the distribution of CCs (left) and RMS errors (right) between DeepIRI and IGS TEC maps (solid line) and between IRI and IGS TEC maps (dotted line) for all test data. In the figure, the CCs between IRI TEC and IGS TEC maps are mostly less than 0.98 and more than half of the RMS errors are larger than 7 TECU. On the other hand, the CCs between DeepIRI TEC and IGS TEC maps are mostly distributed at 0.99. Most of the RMS errors are mostly smaller than 7 TECU, and they are mostly distributed at 4 TECU. Summing up, our model generates the global TEC maps that are much more similar to the IGS TEC ones than the IRI ones. This implies that the DeepIRI TEC maps should be superior to IRI TEC ones.  Table 1, the CC between DeepIRI TEC and IGS TEC maps for validation and test data is higher and the RMSE is smaller than those between IRI TEC and IGS TEC maps. This means that our model improves the IRI TEC map.  Table 2, the CC between DeepIRI TEC and IGS TEC maps for both periods is higher and the RMSE is smaller than those between IRI TEC and IGS TEC maps. This means that our model significantly improves the IRI TEC map not only during solar maximum period but also during solar minimum period.

Summary and Conclusion
In this paper, we have made the model for generating improved IRI TEC maps using a deep learning method based on cGANs. We also quantitatively evaluate our model using simple statistical parameters such as CC and RMSE. The results from this study can be summarized as follows: 1. Our method successfully generates greatly improved IRI TEC maps. 2. The DeepIRI TEC maps that our model generated are quite consistent with the IGS TEC ones. Especially, ionospheric peak structures in both maps are successfully generated while they are not in IRI TEC maps. 3. The differences between DeepIRI and IGS TEC ones are mostly close to 0. In particular, our model greatly improved the IRI TEC at low-latitude region around the equatorial anomaly. 4. Our model shows that the averaged CC is 0.96, and the averaged RMSE is 10.5 TECU for test data set. The model can improve the TEC prediction ability of the IRI-2016. Similarly, we can make an improved model for future IRI-versions.

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The ultimate goal of our study is to generate global TEC maps in near real time. The DeepIRI TEC maps generated in our model are significantly improved than those of the IRI-2016. Our study shows a sufficient possibility to generate global TEC maps in near real time if IRI is generated in time. If global TEC maps are provided in real time, it would be very valuable for space weather monitoring and forecast.