Investigation and Forecasting of Variation in Ionospheric TEC in the Equatorial Region

Abstract

Estimation and prediction of the ionosphere Total Electron Content (TEC) are crucial in improving the accuracy of the Global Navigation satellite systems. The ionosphere TEC causes a group delay in the navigation signal which deteriorates the accuracy of the estimated position. Further, the ionosphere in the equatorial region is highly dynamic and driven by complex electrodynamics like the equatorial ionization anomaly (EIA), equatorial electrojet (EEJ), plasma fountain, etc. which further deteriorate the accuracy and add uncertainties in the estimation of range delays. Currently, the range delay is estimated by using global and regional models based on mathematical formulation and a fixed correction is used to mitigate the error. But these empirical models do not consider the complex spatial and temporal variations in the equatorial ionosphere. To improve accuracy, many data-driven models have also been proposed by erstwhile researchers. Most of the models are long-term prediction models and depend on initial training with large historical data. Since the number of quiet days is much higher as compared to the geo-magnetically disturbed days, the models based on historical data are likely to be biased towards the majority quiet day TEC patterns and may suffer from data bias. Also, such models are usually trained with data for a particular period and require regular retraining. Further, these models are trained on long-term data and hence cannot track the dynamic short-term variations and changing statistical nature of the TEC in the equatorial region. Developing a short-term TEC prediction model trained using the recent variations and irregularities would help improve the prediction accuracy of TEC in an equatorial region. This research work thus focuses on developing forecasting algorithms to extract short-term patterns in TEC in the equatorial region which can provide a basis for range error correction. For developing a short-term prediction model for TEC, the variation pattern, anomalies, correlations, and the temporal dependencies of TEC under quiet and storm conditions were studied for an entire solar cycle of 11 years and also between consecutive solar cycles. Various aspects of the TEC data like the periodicity, short-term irregularities, data imbalance and drift in data over varying time scales were investigated. Different learning strategies and algorithms were explored for developing a prediction model that could adapt to the dynamic nature of TEC in the short term. The findings of this study were used for selecting the relevant data for training the proposed prediction models. Another major challenge in the equatorial region was to identify the predictors for developing the TEC prediction models. Considering the inherent nonlinearities and complexities in the dynamic variables in the equatorial ionosphere due to space weather phenomena like geomagnetic storms, it is difficult to identify variables for the prediction model using the linear correlation method. Hence, the temporal dependence between the variables was investigated during geomagnetic storms and sub-storms. A suitable framework was developed to test the causality between the geomagnetic variables and ionosphere TEC to understand the dynamical response of the ionosphere during storms and sub-storms. From the detailed investigation of the TEC pattern over different time scales, it was observed that the short-term irregularities in the ionosphere had a considerable influence on its dynamic behavior. Hence, in this study, TEC prediction models, built considering short-term irregularities, were developed and evaluated. Various approaches were evaluated for developing short-term prediction models. The approach was to start from the simplest regression model and go further on by adding new model features to address the challenges in the complex dynamic ionosphere. Three regression models with emphasis on insitu learning were developed to track the dynamically changing variation pattern in the incoming TEC. The first regression model was the multistep adaptive segmented forecast model which was developed by using the incoming Vertical total electron content (VTEC) as input in the model fitted with recent past data using the nonlinear regression. The diurnal VTEC for each day was first divided into segments based on the temporal variation pattern using Bayesian optimization. For each segment, a linear or polynomial regression model was fitted using the lag data (lag interval δt =20-30 minutes). The fitted model was then used for predicting VTEC for (t- t+ δt) time interval using the lag VTEC data at time t as input to all the models simultaneously. The predictions of all the models were then compared with the actual data and the model with the lowest residual was selected for the prediction of the VTEC for the next lag interval in that segment. This was recursively applied to all the lag intervals. Thus, the prediction model adaptively learned from the recent variations and irregularities in TEC. The model performance was evaluated for both quiet and geomagnetic storm days for a forecast interval of 20 to 30 minutes. Based on the findings of the causality study, a second forecast model was developed. This model was based on the causal relationship between VTEC and geomagnetic storm variables Dst and AE. To predict TEC one hour in advance, a vectored auto regression model was fitted with causal variables with error corrections. A framework was developed for the selection of lag intervals for causal variables. Long-term dependence was also taken into account by computing the error corrections. Again, the model accuracy was evaluated using the RMSE metric for both quiet and geomagnetic storm days, and the predicted output was verified with the actual GPS VTEC The concept of causality was further extended to design a multivariate auto regression model for an improved prediction interval of TEC. The varying temporal resolution of the dynamic variables Dst, AE, and VTEC has always been a challenge to be used as model parameters for a prediction model. The temporal resolutions of the variables are generally matched by averaging the VTEC data available from dual-frequency receivers and interpolating the geomagnetic variables. The averaging interval is very critical and may result in loss of information during disturbed days (geomagnetic storms) in the equatorial ionosphere where the temporal variation may be as high as 25 TECU for a 1-hour time interval. Thus, a multistep forecast model was developed with rolling features extracted from the past VTEC data without disturbing the temporal scale. The extracted rolling features helped in getting better insights into the variation pattern of the incoming VTEC. The causality framework was then used for selecting suitable features with appropriate lag values. A regression model was fitted using the lag VTEC data along with the causal variables for forecasting TEC for a time interval from ‘t’ to ‘t+ δt’ (δt =20- 45 minutes). The model was fitted recursively with new incoming VTEC at pre-decided time intervals and was evaluated for quiet and storm days with a prediction interval ranging from 20-minutes to 45-minutes depending on the time of the day. A short-term nonparametric model using the machine learning algorithms was also developed for predicting VTEC using feature engineering. Various challenges in developing a prediction model for ionosphere VTEC with machine learning algorithms like data drift, data bias due to rare events, varying temporal scales of input variables, data nonlinearity, interpretability of complex DL models, training time, and retraining were taken into consideration. The main objective was to develop a short-term model for the TEC prediction that was simple and was able to track the dynamics of the equatorial ionosphere with fair prediction accuracy. The model was developed with two different approaches. First, a short-term multiclass classifier was developed by learning the temporal pattern in the VTEC by extracting subsequence from the diurnal VTEC and transforming each subsequence into an output class. The classifier model was developed to predict the VTEC class 30 minutes in advance. The classifier model was developed using SVM and RF algorithms. This model was then extended to develop the the second model where the regression between the features extracted from the past VTEC was used to predict VTEC 30 minutes in advance for the next five consecutive days’ subject to quiet conditions of the ionosphere. The model performance was evaluated using precision, recall, and ROC. The second model was thus developed using the SVM and RF regression algorithms by learning the temporal sequence in VTEC over a given period. Considering the importance of bias-variance tradeoff, both the models used seasonal VTEC data so that the seasonal and yearly drifts could be accounted for. Further, since these drifts require regular retraining of models, the use of short-term data reduced the training time. Features were extracted using a fixed lag interval to get more insights into the variation pattern of VTEC. The derived features along with the variables describing the solar and geomagnetic influences on VTEC were used as input for training the model. The model performance was evaluated using the RMSE of the predicted VTEC with the actual GPS VTEC. The performance of the model was comparable to DL models with a diurnal RMSE of less than 10 TECU for the geomagnetic storm days. The major focus and contribution of this work have been to provide an insight into the various aspects and interdependencies of the TEC influencing ionosphere parameters under varying ionosphere conditions. This will be of great use in identifying and selecting training parameters when developing a forecast model for VTEC. Based on the finding, improved short-term prediction models were designed and developed which counter the effects of models trained on long-term data with complex machine learning approaches. The proposed models were simple, easy to interpret, and performed well with regular retraining with a smaller dataset.