A THREE-DIMENSIONAL APPROACH TO IMPROVE THE INTERNATIONAL REFERENCE IONOSPHERE (IRI) MODEL

Research on total electron content (TEC) empirical models is one of the important topics in the field of space weather services. Global TEC empirical models based on Global Ionospheric Maps (GIMs) TEC data released by the International GNSS Service (IGS) have developed rapidly in recent years. However, the accuracy of such global empirical models has a crucial restriction arising from the non-uniform accuracy of IGS TEC data in the global scope. Specifically, IGS TEC data accuracy is higher on land and lower over the ocean due to the lack of stations in the latter. Using uneven precision GIMs TEC data as a whole for model fitting is unreasonable. Aiming at the limitation of global ionospheric TEC modelling, this paper proposes a new global ionospheric TEC empirical model named the TECM-GRID model. The model consists of 5183 sections, corresponding to 5183 grid points (longitude 5°, latitude 2.5°) of GIM. Two kinds of single point empirical TEC models, SSM-T1 and SSM-T2, are used for TECM-GRID. According to the locations of grid points, the SSM-T2 model is selected as the sub-model in the Mid-Latitude Summer Night Anomaly (MSNA) region, and SSM-T1 is selected as the sub-model in other regions. The fitting ability of the TECM-GRID model for modelling data was tested in accordance with root mean square (RMS) and relative RMS values. Then, the TECM-GRID model was validated and compared with the NTCM-GL model and Center for Orbit Determination in Europe (CODE) GIMs at time points other than modelling time. Results show that TECM-GRID can effectively describe the Equatorial Ionization Anomaly (EIA) and the MSNA phenomena of the ionosphere, which puts it in good agreement with CODE GIMs and means that it has better prediction ability than the NTCM-GL model.

In this article, we analyze vertical total electron content (VTEC) over Nepal for 4 periods: March 14–25, 2015, June 18–29, 2015, May 24–June 4, 2017, and September 3–14, 2017. In each period, there are quiet geomagnetic days and intense geomagnetic stormy days. The VTEC observed during these periods has observed both positive and negative ionospheric storms. We compared VTEC Receiver-Independent Exchange Format (RINEX) observations with the Global Ionospheric Map (GIM), Centre for Orbit Determination in Europe (CODE), and IGS working group (IGSG). We found in RINEX observation of the VTEC a noon bite out profile with predominance of morning and afternoon peaks and a nighttime peak, but this was not noticeable clearly with CODE and IGSG models. The comparison between RINEX TEC, CODE, and IGSG models shows that the GIM model does not estimate RINEX VTEC over Nepal. The disagreement between VTEC CODE/IGSG and VTEC RINEX is important during geomagnetically quiet periods, while there is good agreement between VTEC CODE/IGSG and VTEC RINEX during strong geomagnetic storms. We also find a greater disagreement between the models and the data at the equinoxes when the VTEC is larger. It is, therefore, necessary to introduce data from Nepal stations into the models CODE and IGSG in order to improve them.

Two major earthquakes separated by ∼5 minutes occurred in the same fault in Peru at depths of 606.2 and 620.6 km on November 24, 2015. By using Global Ionospheric Maps (GIMs) from the Center for Orbit Determination in Europe (CODE) and a broadly used statistical method, differential Vertical Total Electron Content (VTEC) maps were derived. Two positive ionospheric anomalies were clearly identified in the differential VTEC maps 2 and 1 day prior to the day of the earthquakes. These anomalies were located inside the earthquakes’ preparation regions defined by the Dobrovolsky equation. On the other hand, due to the low-latitude nature of the seismic events, the Equatorial Ionization Anomaly (EIA) shape was also analyzed. A third positive disturbance was revealed between November 20 and 21, 2015. For the aforementioned anomaly and the one on November 22 (2 days before the earthquakes), an enhancement of the VTEC was observe through the considerable modification of the EIA shape into a well-defined double-crest with a trough. By looking into the Dst and Kp indices, the geomagnetic conditions starting on November 20 until the 24 were very quiet; thus, it is considered that the three detected anomalies are precursors to the earthquake doublet. Moreover, it is suggested that the mechanism at work that produced the positive disturbances is the air ionization through the release of radon from the Earth’s crust.

Dual-frequency global navigation satellite systems (GNSS) observations provide most of the input data for development of global ionosphere map (GIM) of vertical total electron content (VTEC). The international GNSS service (IGS) develops different ionosphere products. The IGS tracking network stations are not homogeneously distributed around the world. The large gaps of this network in Middle East, e.g., Iran plateau, reduce the accuracy of the IGS GIMs over this region. Empirical ionosphere models, such as international reference ionosphere (IRI), also provide coarse forecasts of the VTEC values. This paper presents a new regional VTEC model based on the IRI 2007 and global positioning system (GPS) observations from Iranian Permanent GPS Network. The model consists of a given reference part from IRI model and an unknown correction term. Compactly supported base functions are more appropriate than spherical harmonics in regional ionosphere modeling. Therefore, an unknown correction term was expanded in terms of B-spline functions. The obtained results are validated through comparison with the observed VTEC derived from GPS observations.

Global ionosphere models may not be accurate enough in regions where there are insufficient observations. Therefore, there is strong interest in regional ionosphere modeling using observations from dual-frequency Global Navigation Satellite System (GNSS) receivers in such regions. This paper presents a data assimilation method for hourly total electron content (TEC) modeling along with estimation of the receivers’ differential code biases (DCBs). For this purpose, first, initial values for slant TEC (STEC) and the receivers’ DCBs are estimated utilizing global ionosphere maps (GIMs). Second, STEC is expanded to a linear combination of spherical radial basis functions with time-dependent coefficients to reduce the number of unknowns, and a constrained least-squares adjustment is applied to resolve the corrected STEC and DCB values in the study area using observations from dual-frequency GNSS receivers. Third, the resolved STEC at ionospheric pierce points (IPPs) are converted to vertical TEC (VTEC) using a mapping function and assimilated into the background provided by spatial and temporal interpolation of GIM. Retrieved VTECs are weighted according to the satellites’ elevation angles, and an objective function is defined to determine the background’s covariance matrix. In this study, the Iranian permanent Global Positioning System (GPS) network is used to construct the regional hourly VTEC model and calculate hourly DCB variations. The proposed method is validated in two ways. First, some of the VTEC values are excluded from the dataset for use as test data and compared with modeling results. The root mean square (RMS) of the constructed regional assimilative model on test data is significantly better than GIM. Second, the RINEX file of Tehran station, whose observations did not play a role in modeling, is corrected using the regional model. The single-frequency positioning results with corrected observations show much better accuracy than GIMs.

Combination of swarm, Jason-3, and GNSS observations to construct a new modeling of global ionospheric maps

Temporal extrapolation of TEC using WNN during 2007–2018 and comparison against GIM, IRI2016 and Kriging

The ionosphere, crucial for satellite navigation and radio communication, is highly sensitive to solar and geomagnetic activities. Traditional ionospheric prediction models often struggle to capture its complexities. This paper introduces a Graph-Enabled Spatio-temporal transformer (GEST) model, designed to predict the Total electron content (TEC) in the ionosphere with higher accuracy. The GEST model innovatively integrates six dynamic space weather parameters, including the Kp index, and refines grid distances and weights in the Global ionospheric maps (GIM). Leveraging the efficiency of the Transformer architecture in processing spatio-temporal data, the GEST model adapts to varying ionospheric conditions and provides superior precision. Our evaluations, based on data from the Center for orbit determination in Europe (CODE), demonstrate that the GEST model significantly outperforms traditional methods and other intelligent algorithms such as conv-LSTM. It shows marked improvements in Mean absolute error (MAE), Root mean square error (RMSE), Pearson correlation coefficient (CC), and Mean absolute percentage error (MAPE), particularly during periods of intense solar and geomagnetic activity. These advancements highlight the GEST model’s substantial contributions to the field of ionospheric prediction technology, offering a robust tool for enhancing the reliability of satellite-based systems.

Negative VTEC with spherical harmonic expansion model under different solar activity conditions

Choi et al. (2019) suggested that ionospheric total electron content (TEC) and receiver differential code bias (rDCB) stability have a strong correlation during a period of two years from 2014 to 2016. This article is a response to Zhong et al. (2020), who pointed out that the long-term variations of the GPS DCBs are mainly attributed to the satellite replacement rather than the ionospheric variability. In this issue, we investigated the center for orbit determination in Europe (CODE) Global Ionosphere Maps (GIM) products from 2000 to 2020. In this study, changes in TEC and receiver DCB (rDCB) root mean squares (RMS) at Bogota (BOGT) station still have a clear correlation. In addition, there was a moderate correlation between satellite DCB RMS and rDCB RMS. As a result, we suggest that rDCB can be affected simultaneously by GPS sDCB as well as ionospheric activity.

Geodetic very long baseline interferometry (VLBI) observations are carried out, with the legacy system, using two well‐separated frequency bands in order to determine first‐order ionospheric delay corrections corresponding to the combined effect of total electron content (TEC) at two stations forming a baseline. On the other hand, it is possible to obtain the vertical TEC (VTEC) above the VLBI antennas from VLBI data. This research intends to investigate the role of the ionospheric spatial gradient on VTEC which is derived from VLBI observations based on the latest four Continuous VLBI Campaigns (CONT08 to CONT17‐L1). For this purpose, station‐based VTEC values were computed in two modes, with and without spatial gradients. Then, these two approaches were evaluated by comparison to global ionospheric maps (GIMs). The differences between the GIM‐based VTEC values and the VLBI VTEC values derived using two parameterization approaches were used to compute the Root Mean Square Error (RMSE) for each VLBI station during the CONTs. In addition, the improvement percentages of the VLBI VTEC's error were calculated to understand the spatial gradient role. Based on the obtained results, the role of spatial gradient is more significant on the equatorial region as compared to the polar area. Using the ionospheric spatial gradient decreases the RMSE values of VLBI‐derived VTEC values from CONT08, CONT11, CONT14, and CONT17‐L1 by 26.4%, 37.6%, 32.4%, and 27.4%, respectively. In addition, it is also shown that this parameter reduces the RMSE values during the high solar activity, as in 2011 and 2014.

<p>The vertical total electron content (VTEC) is one of the main quantities to describe the state of the ionosphere. To dispose this information is important to mass market Global Navigation Satellite System (GNSS) users to correct the ionospheric delay for positioning. The VTEC values and the corresponding standard deviations are routinely provided in the so-called Global Ionosphere Maps (GIM), with time intervals of 2, 1 and 0.25 hours on regular grids with 2.5º resolution in latitude and 5º resolution in longitude. To determine the ionospheric corrections from the GIMs for positioning applications, a quadratic interpolation is typically applied to the VTEC grid values which generally does not take into account the VTEC uncertainties. In this context, the impact of the use of the VTEC standard deviation is assessed in the positioning domain, considering the GIMs of two different analysis centers. The impact of the VTEC uncertainties is analyzed by means of single-frequency precise point positioning (PPP), applied to four Brazilian GNSS stations in different regions, considering four scenarios: geomagnetic storm, low solar flux and high solar flux (equinox and solstice). The use of the VTEC uncertainties values provided a significant improvement coinciding with high solar flux, especially for stations in regions under the most intense ionospheric effect, with mean rates of improvements up to 47%.</p>

Validation of CAS’s final global ionospheric maps during different geomagnetic activities from 2015 to 2017

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 has a spatial resolution of 5° longitude and 2.5° latitude, with a time resolution of 1 h. We utilized the Center for Orbit Determination in Europe (CODE) GIM dataset for 18 years from 2002 to 2019, without requiring any other external input parameters, to train the ConvLSTM models for forecasting GIM 1, 2, and 3 days in advance. Using the CODE GIM data from 1 January 2020 to 31 December 2023 as the test dataset, the performance evaluation results show that the average root mean square errors (RMSE) for 1, 2 and 3 days of forecasts are 2.81 TECU, 3.16 TECU, and 3.41 TECU, respectively. These results show improved performance compared to the IRI-Plas model and CODE’s 1-day forecast product c1pg, and comparable to CODE’s 2-day forecast c2pg. The model’s predictions get worse as the intensity of the storm increases, and the prediction error of the model increases with the lead time.

Ionospheric delay poses significant challenges for satellite‐based communication and navigation applications. Predicting the global ionosphere variation can help to capture the vertical total electron content (VTEC) in advance, which improves the signal stability of communication and navigation, and supports these space‐related technologies. In existing studies, the ConvLSTM‐based method has achieved impressive results in global ionosphere map (GIM) prediction and gained increasing attention. However, the ConvLSTM model can only consider local features in GIM prediction since the single layer Convolutional Neural Network structure in ConvLSTM can not capture the global features. Inspired by the ResNet and the SimVP models, this paper proposes a new TEC prediction method based on a large receptive field model named large receptive field model with residual structure (LARRES). This method achieves a large receptive field effect through a deep global spatio‐temporal convolutional network, which allows to capture the global TEC features during the prediction process. The prediction performance of the LARRES model was evaluated with 8 years GIM data in both high and low solar activity years. The experimental results show that the proposed model outperforms the C1PG model from Center for Orbit Determination in Europe and two ConvLSTM‐based models. Compared to the C1PG model, the LARRES method can reduce RMS error by 28.7% and 10.4% during high and low solar activity years, respectively. The LARRES method can further reduce the global TEC prediction error by 0.35 TECU and 0.08 TECU subject to the ConvLSTM‐based models during high and low solar activity years respectively.