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Prediction performance of convolutional long short‐term memory (convLSTM)‐Lc, convLSTM‐L1, convLSTM‐L2, and the persistence models under weak (a), moderate (b), and strong (c) ionospheric irregularity levels.
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This study presents an image‐based convolutional long short‐term memory (convLSTM) machine learning algorithm to predict storm‐time ionospheric irregularities. Unlike existing methods that are either focused on irregularities at individual locations or treat the irregularity prediction as a classification problem, the convLSTM‐based architecture fo...
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Total electron content (TEC) is one of the most important parameters of the ionosphere, which reflects the main characteristics of the ionosphere. Its accurate prediction plays an important role in improving the accuracy of GNSS navigation and ensuring the remote communication of radio. In order to solve the problems that the current combination of...
Space launches produce ionospheric disturbances which can be observed through measurements such as Global Navigation Satellite System signal delays. Here we report observations and numerical simulations of the ionospheric depletion due to a Small-Lift Launch Vehicle. The case examined was the launch of a Rocket Lab Electron at 22:30 UTC on March 22...
In this paper, we propose a global ionospheric total electron content (TEC) maps (GIM) prediction model based on deep learning methods that is both straightforward and practical, meeting the requirements of various applications. The proposed model utilizes an encoder-decoder structure with a Convolution Long Short-Term Memory (ConvLSTM) network and...
This paper introduces a novel technique that uses observation data from GNSS to estimate the ionospheric vertical total electron content (VTEC) using the Kriging–Kalman method. The technique provides a method to validate the accuracy of the Ionospheric VTEC analysis within the Equatorial Ionization anomaly region. The technique developed uses GNSS...
Citations
... They predicted IS with an 81 % accuracy and an 80 % accuracy for the ROTI. A forecasting model of irregularity structures in the mid and high latitudes was developed by Liu et al. (2021). They used 550 GNSS stations installed at (45°-90°N, 0°-180°W) for six months of sample data in 2015. ...
... Their work differs from ours, especially with the shorter 1-h lead time, using phase index and considering the high latitudes where the ionospheric electrodynamics differ. A storm time ROTI model was developed by Liu et al. (2021) using some 8 months of ROTI data and convolutional LSTM evaluated with a customdesigned loss function. Their model was developed on disturbed conditions and in the high latitudes in contrast to our quite time considerations in the low-latitude region where the underlying physics differs. ...
... Thirdly, almost all preexisting works, except those that employ images, rely on solar wind parameters for irregularity pattern inferences, meaning that, in the absence of these parameters, making realistic projections are limited. The rationale emerges then that "in the absence of solar wind parameters, we opt for image-based approaches" comparable to the work of Liu et al. (2021). Unfortunately, the complexities and computational cost in preprocessing these images, the training time and resources required to execute a single convolutional network coupled with the expertise required, prompt the exploration of alternative approaches. ...
This study explores machine learning models to gain insights into dynamics of ionospheric irregularities over geodetic receivers in Mbarara (0.60° S, 30.74° E) and Kigali (1.94° S, 30.09° E). A seven-year rate of total electron content index (ROTI) database and two modeling approaches (multivariate and univariate) were employed. The motivation was to treat the database with time series techniques following a case study with and without the influence of solar wind parameters. The objective is to examine how each approach reconstructs the morphology of ROTI within 3-h time steps over a 24-h cycle. To achieve this, five machine learning models, including extreme gradient boosting (XGBoost), random forest (RF), bidirectional long-short term memory (BLSTM), unidirectional long-short term memory (LSTM) and nonlinear autoregressive with eXogenous input (NARX), were developed and evaluated. Test results demonstrate significant performance variations highlighting comparable ROTI reconstructions in the absence of the solar wind features. The RF model exhibited superior performance with the lowest mean absolute errors of 0.03 and 0.07 TECU/min and accuracies of 93% and 75% under multivariate and univariate modeling, respectively. Based on the RF model’s performance, we employed an extended database over the Ugandan (Mbar) station for further model development and validated its efficiency over a station in Rwanda (Nurk). The results provided promising insights, emphasizing the need for future research dedicated to robust and enhanced nowcasting models that leverage long-term ionospheric data, especially in regions with limited scintillation monitors.
... In order to predict the size of the ionospheric anomalies, the authors of Liu et al. (2021) created a loss function that was incorporated into an image-based machine learning model. The forecasting accuracy was analyzed for a lead time of 10-60 minutes. ...
We design physics-informed loss functions for training Artificial Neural Network (ANN) models to forecast the ionospheric vertical Total Electron Content (vTEC) from 1 to 24 hours in advance. The ANN models exploit our physics-informed loss functions, data provided by the Global Navigation Satellite Systems (GNSS) receiver installed at Tsukuba (36.06o\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{o}$$\end{document} N, 140.05o\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{o}$$\end{document} E), Japan, and external drivers (solar and geomagnetic indices). The time series used span from January 1, 2006, to December 31, 2018, i.e., a full solar cycle. A proper set of external drivers for the ANN models training are selected by ranking their importance in relation to the vTEC dynamics at different forecasting horizons. They result to be the 10.7 cm Solar Flux (F10.7), the magnitude of the Interplanetary Magnetic Field (IMF) BT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\boldsymbol{B}_{\boldsymbol{T}}$$\end{document}, and the Auroral Electrojet (AE) index. Moreover, a second set of indices among those available has been considered as constraints in the design of the physics-informed loss functions. They are the Disturbance Storm Time (Dst) index, the solar wind speed v,BT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\boldsymbol{v}, \boldsymbol{B}_{\boldsymbol{T}}$$\end{document}, and the By and Bz components of the interplanetary magnetic field. To assess the performance of the resulting ANN models, we use the statistical parameter coefficient of determination (R2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\boldsymbol{R}^{{\textbf {2}}}$$\end{document}), the standard deviation (SD), and the Wilcoxon non-parametric signed ranked test. We show that, in the testing period analyzed (from 2017-09-13, at 04:40:00, to 2018-12-31, at 23:55:00), one of our physics-informed loss functions provides a better performance of the ANN with regard to the standard loss function commonly adopted. In particular, when the new loss function is used in the ANN model, the average SD is minimized across all forecasting horizons in the training, validation and test datasets. SD is 0.2560 TECU, 0.3183 TECU and 0.4240 TECU for the training, validation and test dataset respectively, where 1 TECU = 1016\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\textbf {10}}^{{\textbf {16}}}$$\end{document} electrons/m2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\boldsymbol{m}^{{\textbf {2}}}$$\end{document}. The ANN model, incorporating the new loss function and applied to the test dataset, shows a significant improvement according to the Wilcoxon signed ranked test. In fact by selecting a significance level α=0.05\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\boldsymbol{\alpha }~ \mathbf {= 0.05}$$\end{document}, the probability to obtain results by chance with the new loss function as compared to the standard loss function is 0.01504 (i.e., <α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$<\alpha $$\end{document}), which implies that the new loss function gives a statistical improvement to the forecasting capability of the ANN model. To the best of our knowledge, this is the first time a physics-informed loss function has been designed for the task of forecasting the ionospheric vTEC.
... Additionally, obtaining high-sampled measurements of ionospheric irregularities based on the global navigation satellite systems (GNSS) monitor networks is still difficult. Therefore, forecasting short-time ionospheric irregularities is still a big challenge [23], [24], [25]. ...
... Atabati et al. [30] implemented by combining an ANN with the genetic algorithm to predict the ionospheric scintillation based on the signal-to-noise ratio or the ROTI data of the single GNSS station-GUAM. Liu et al. [25] presented an image-based convolutional long short-term memory algorithm to forecast the regional ionospheric irregularities from ROTI maps in high latitudes, which does not incorporate various influencing factors, such as solar and geomagnetic activity observations and so on, into the proposed model. ...
... Those abovementioned studies mainly consider the ionospheric irregularity forecasting as classification problems [29], predict ionospheric irregularities based on the single/two GNSS monitors [26], [30], or do not take into account the complicated relationship between the ionospheric irregularities and various influencing factors [25]. In this regard, a hybrid ensemble model (HEM) is implemented to forecast the occurrence and intensity of ionospheric irregularities [25], [26] rather than as a classification consideration at the equator and low latitudes. ...
Accurate and timely forecasting of ionospheric irregularities is of great significance for the reliable and stable operation of global high-precision communication and navigation systems at low latitudes. In this study, we implement a hybrid ensemble model (HEM) that combines multiple machine learning models for forecasting the occurrence and intensity of ionospheric irregularities instead of considering ionospheric irregularity forecasting as classifications. Meanwhile, this model is trained with the GNSS-derived rate of total electron content index (ROTI) maps from approximately 147 ground-based global navigation satellite systems (GNSS) receivers in Brazil sector (35°S-5°N, 30°W-75°W). Meanwhile, a diverse set of input features including interplanetary magnetic field (IMF) components, F2 layer critical frequency (foF2), peak height F2-layer (hmF2), F10.7, flow pressure, and SYM-H indices during January 1 to October 31, 2022. Regarding the relative importance of various input features, results demonstrate that the performance of the HEM model trained by the ROTI and hmF2 observations for predicting ionospheric irregularities is superior to that of other input features. Furthermore, the deviations of forecasting ionospheric irregularities from the HEM model occur mainly in the southern equatorial ionization anomaly regions, and the accuracy of the HEM model with daily standard deviation (STD) and root mean square (RMS) less than 0.1 TECU/min. Hence, the HEM model is more stable and greater than other predicted models. Additionally, the HEM algorithm can forecast the ionospheric irregularity structures and intensity for 30 minutes over Brazilian territory. It is expected to improve the accuracy of short-term ionospheric irregularities forecasting at low latitudes.
... de Paulo et al. (2023) employed an encoder-decoder ConvLSTM network architecture to accomplish a one-day global TEC forecast by using multiple days of GIMs. Furthermore, the multi-channel ConvLSTM networks that combine features such as solar and geomagnetic indices have demonstrated advantages in predicting TEC evolution and ionospheric irregularities during storms (Gao and Yao 2023;Liu et al. 2021). In the above studies, large-scale ionospheric oscillations due to solar activity and space weather were well predicted, but the forecasting of small-scale and shortterm ionospheric disturbances associated with lower atmospheric activities were rarely investigated. ...
... The BatchNormalization layer normalizes the data to expedite training and enhance the stability of the model. The architecture of the three hidden layers strikes a balance between ensuring model complexity to better capture spatiotemporal relationships in the data and maintaining computational cost efficiency (Chen et al. 2022a;Gao and Yao 2023;Liu et al. 2021). The output layer is a fully connected layer that applies the 'linear' activation function and outputs 2-channel forecast results through two 1 × 1 filters. ...
The uneven distribution of GNSS observations and the scarcity of satellite data pose challenges for the continuous detection of traveling ionospheric disturbances (TIDs) induced by gravity waves (GWs). This paper proposes a short-term TID forecasting method based on the convolutional long short-term memory (ConvLSTM) neural network. This method utilizes 3-D electron density disturbance information from 3-dimensional computerized ionospheric tomography (3DCIT) results to predict the 3-D characteristics of ionospheric disturbances during Hurricane Matthew. A multi-channel forecasting pattern combining disturbance feature labels is used to improve the forecast accuracy. The results show that the ConvLSTM network can effectively identify the spatiotemporal features of TIDs. The inclusion of the labels greatly enhances the forecast performance, as shown by the reduction of the mean absolute error (MAE) and root mean square error (RMSE) over longer forecast durations, along with the increase in correlation. Additionally, the horizontal phase velocities of the TIDs at 200 and 300 km altitudes calculated using the 5-minute forecast results (∼150-173.33 m/s) are comparable to the original 3DCIT estimation (∼166.67-170 m/s).
... To address this limitation and balance the spatiotemporal characteristics of time series data, Shi et al. [28] introduced convolutional operations into LSTM and designed a ConvLSTM structure, which effectively utilizes spatiotemporal correlation in time series prediction. Liu et al. [29] proposed an innovative image-based ConvLSTM model to predict storm time ionospheric irregularities. The ConvLSTM structure outperforms the time series prediction model in precipitation prediction. ...
Total electron content (TEC) is a vital parameter for describing the state of the ionosphere, and precise prediction of TEC is of great significance for improving the accuracy of the Global Navigation Satellite System (GNSS). At present, most deep learning prediction models just consider TEC temporal variation, while ignoring the impact of spatial location. In this paper, we propose a TEC prediction model, ED-ConvLSTM, which combines convolutional neural networks with recurrent neural networks to simultaneously consider spatiotemporal features. Our ED-ConvLSTM model is built based on the encoder-decoder architecture, which includes two modules: encoder module and decoder module. Each module is composed of ConvLSTM cells. The encoder module is used to extract the spatiotemporal features from TEC maps, while the decoder module converts spatiotemporal features into predicted TEC maps. We compared the predictive performance of our model with two traditional time series models: LSTM, GRU, a spatiotemporal mode1 ConvGRU, and the TEC daily forecast product C1PG provided by CODE on a total of 135 grid points in East Asia (10°–45°N, 90°–130°E). The experimental results show that the prediction error indicators MAE, RMSE, MAPE, and prediction similarity index SSIM of our model are superior to those of the comparison models in high, normal, and low solar activity years. The paper also analyzed the predictive performance of each model monthly. The experimental results indicate that the predictive performance of each model is influenced by the monthly mean of TEC. The ED-ConvLSTM model proposed in this paper is the least affected and the most stable by the monthly mean of TEC. Additionally, the paper compared the predictive performance of each model during two magnetic storm periods when TEC changes sharply. The results indicate that our ED-ConvLSTM model is least affected during magnetic storms and its predictive performance is superior to those of the comparative models. This paper provides a more stable and high-performance TEC spatiotemporal prediction model.
... EPBs are a known cause of radio wave scintillations (Kintner et al., 2007), and ML has been used to predict when and where scintillations may occur (Jiao et al., 2017;Linty et al., 2018;McGranaghan et al., 2018). Lastly, deep learning has also been applied to predict storm-driven irregularities within the ionosphere (Liu et al., 2021). ...
In this study we present AI Prediction of Equatorial Plasma Bubbles (APE), a machine learning model that can accurately predict the Ionospheric Bubble Index (IBI) on the Swarm spacecraft. IBI is a correlation (R²) between perturbations in plasma density and the magnetic field, whose source can be Equatorial Plasma Bubbles (EPBs). EPBs have been studied for a number of years, but their day‐to‐day variability has made predicting them a considerable challenge. We build an ensemble machine learning model to predict IBI. We use data from 2014 to 2022 at a resolution of 1s, and transform it from a time‐series into a 6‐dimensional space with a corresponding EPB R² (0–1) acting as the label. APE performs well across all metrics, exhibiting a skill, association and root mean squared error score of 0.96, 0.98 and 0.08 respectively. The model performs best post‐sunset, in the American/Atlantic sector, around the equinoxes, and when solar activity is high. This is promising because EPBs are most likely to occur during these periods. Shapley values reveal that F10.7 is the most important feature in driving the predictions, whereas latitude is the least. The analysis also examines the relationship between the features, which reveals new insights into EPB climatology. Finally, the selection of the features means that APE could be expanded to forecasting EPBs following additional investigations into their onset.
... Chen et al. (2022a, b) have combined the ConvLSTM network with spectrum analysis for ionospheric TEC using data sets from 2015 to 2019. Liu et al. (2021) have used the ConvLSTM network with a custom-design loss function to forecast the ROTI maps over high latitudes and results show that this model has a good prediction performance on ionospheric irregularities. However, these studies are still needed to consider the solar and geomagnetic activity indices to improve the generalization performance of the model. ...
The total electron content (TEC) is an important parameter for characterizing the morphology of the ionosphere. Modeling the ionospheric TEC accurately during the storm time could contribute to the operation of global navigation satellite systems (GNSS), satellite communications, and other applications. This study uses an image-based convolutional long short-term memory (ConvLSTM) network with multichannel features to forecast ionospheric TEC during the quiet periods and storm periods. The sunspot number (SSN), solar wind velocity (Vsw), Dst, and Kp geomagnetic indices are firstly fed into the model as the channel features to improve generalization performance. Based on the variation of the Dst index, we have collected gridded TEC maps from 2011 to 2018 with a 1-h interval from the global ionospheric maps (GIM) as the data set including quiet periods and storm periods of ionospheric TEC. The performance of the ConvLSTM model in forecasting TEC is also compared with other deep learning models such as LSTM, gated recurrent unit (GRU), and LSTM-CNN. Furthermore, the accuracy consistency of the ConvLSTM model during the different phases of the storm period is also evaluated for the different output steps of predicted TEC maps. The optimal combination of input features for the model is also investigated during the storm period. Testing results show that the ConvLSTM network with multichannel features has good prediction performance for quiet periods and storm periods by incorporating both solar and geomagnetic activity indices. The statistical indicators show that the ConvLSTM model performs well with lower mean absolute error (MAE), root mean square error (RMSE), and larger correlation coefficient (R) compared with other methods. We have demonstrated that the model with a larger prediction step has worse prediction performance at the low-latitude area, especially during the storm period. In our future work, the larger TEC data set and more solar and geomagnetic indices will be investigated.
Highlights
An image-based convolutional long short-term memory (ConvLSTM) network with multichannel features for forecasting ionospheric TEC.
Solar and geomagnetic indices as the input features for improving the performance of the model.
The ConvLSTM model has good prediction performance for quiet and storm periods by incorporating both solar and geomagnetic activity indices.
... The convLSTM architecture is capable of learning features from a spatiotemporal sequence. It has been successfully applied in many fields of multi-dimensional spatiotemporal predictions (Shi et al., 2015(Shi et al., , 2017Liu et al., 2021). In this study, the convLSTM layer is used as the core module to predict global TEC maps. ...
... The encoder parts are then unfolded using the decoder blocks to predict 24 future maps, which are elements of the output (̂2 5,̂26, . . . ,̂47,̂48 ) shown in Figure 3. Detailed descriptions of this architecture can be found in Shi et al. (2015) and Liu et al. (2021). Here, two prediction strategies are implemented to predict global TEC maps. ...
This paper applies the convolutional long short‐term memory (convLSTM)‐based machine learning models to forecast global ionospheric total electron content (TEC) maps with up to 24 hr of lead time at a 1‐hr interval. Four convLSTM‐based models were investigated, and the one that implements the L1 loss function and the residual prediction strategy demonstrates the best performance. The convLSTM models are trained and evaluated using Center for Orbit Determination in Europe (CODE) global TEC maps over a period of nearly seven years from 19 October 2014 to 21 July 2021. Results show that the best convLSTM model outperforms the 1‐day predicted global TEC products released by CODE analysis center (c1pg) and persistence models under various levels of solar and geomagnetic activities, except for a lead time beyond 8 hr during the storm time where the c1pg has slightly better performance. The convLSTM forecasting performance degrades as the lead time increases.
... AI) (Chai et al., 2020;Hu et al., 2021;Ravuri et al., 2021;Rouet-Leduc et al., 2020;L. Liu et al., 2020;Vech & Malaspina, 2021). The rapid progress in AI research has substantially impacted many scientific fields, including geophysical sciences, on account of the increase in data and serious computational power (Kadow et al., 2020;Lee et al., 2021;L. Liu et al., 2021;Reichstein et al., 2019;Sai Gowtam & Tulasi Ram, 2017). Examples include unsupervised learning to classify seismic events (Cui et al., 2021), deep convolutional neural networks for the recognition of extreme events such as coronal mass ejections (Wang et al., 2019) and predicting storm-time ionospheric irregularities using image-based co ...
The ionospheric sporadic E layer, the ionospheric irregularities of enhanced electron density, appears in the Earth’s ionosphere at altitudes between 90 and 120 km, which supports the real-world radio communication needs of many sectors reliant on ionosphere-dependent decision-making. The prediction of the occurrence of sporadic E layers has been extremely difficult due to the highly complex behavior. Conventional numerical methods are limited because of the inability to extract high-level information from data. Deep learning is a powerful tool for mining latent features from data, which can theoretically avoid assumptions constraining physical methods. Inspired by feature extraction, we applied deep learning to explore latent relationships between mapping observable lower atmospheric data and ionospheric data from limited observations. The proposed model was trained with high-resolution ERA5 data during Jan. 1, 2007-Aug. 30, 2018 as input and corresponding ionospheric sporadic E data collected from COSMIC RO measurements as output. The results show that the model can learn complex relevance as bridges connecting the input and the desired output and obtain excellent performance and generalization capability by applying multiple evaluation criteria. Additionally, we established several model architecture training methods to explore the performance of the model with different input data. The statistic results show that model inference performance is proportional to the abundance of input information and is impacted by intraseasonal variability. The inference capability of the model achieves the best performance in the Jun.-Aug. (JJA) and Dec.-Feb. (DJF) seasons, which is the exact period of sporadic E layer significant occurrence, although different models are evaluated.
