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When using predicted total electron content (TEC) products to generate preliminary real-time global ionospheric maps (GIMs), validation of these ionospheric predicted products is essential. In this study, we evaluate the accuracy of five predicted GIMs, provided by the international GNSS service (IGS), over continental and oceanic regions during th...
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Due to the differences of ionospheric modeling methods and selected tracking stations, the accuracy and consistency of Global Ionospheric Maps (GIMs) released by Ionosphere Associate Analysis Centers (IAACs) are different. In this study, we evaluate and analyze in detail the accuracy and consistency of GIMs final products provided by six IAACs from...
We analyse day-today variability in total electron content (TEC) values measured at five GPS stations in the equatorial region for 90 days in 2008 (day 32 to day 122). The spectral analysis identifies periodicities of 9, 13-14.5 and 21-22 days in the data at five stations. These periodicities are primarily associated with changes in the solar wind...
The low-latitude ionosphere is a dynamic region with a wide range of disturbances in temporal and spatial scales. The Giant Metrewave Radio Telescope (GMRT) situated in the low-latitude region has demonstrated its ability to detect various ionospheric phenomena. It can detect total electron content (TEC) variation with precision of 1 mTECU and also...
In this study, Global Ionosphere Specification (GIS) based on Gauss‐Markov Kalman filter assimilation of slant total electron content observed from ground‐based global positioning system receivers and space‐based radio occultation instrumentations is applied to investigate the ionospheric day‐to‐day tidal variability during the 2009 stratospheric s...
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... Also, the accuracy of the generated RT-GIM is slightly better than that of predicted GIMs (M. Li et al., 2018). ...
This study applies the zero‐differenced integer ambiguity method, named PPP‐Fixed, to extract real‐time ionospheric data and eliminate the latencies of rapid/final Global Ionosphere Maps (GIMs). The PPP‐Fixed method is also used to derive ionospheric data for post‐processed GIM generation, named SGG Post‐GIM, combined with low earth orbit satellite data. The obtained hardware delays are applied to revise real‐time ionospheric data. Meanwhile, the estimated multi‐source ionospheric model is regarded as historical data to estimate an ionospheric prediction model for constraint using the semi‐parameter model. Then, the Kalman filter is employed to estimate the parameters to generate real‐time GIM. Finally, the accuracy of estimated real‐time GIM, named SGG RT‐GIM, and SGG Post‐GIM is assessed. During the experimental period, the mean differences of SGG Post‐GIM and SGG RT‐GIM relative to GIMs provided by the international Global Navigation Satellite System service, named IGSG, are −0.46 and −0.57 Total Electron Content Unit (TECU), respectively. The corresponding Root Mean Square (RMS) values are 1.64 and 3.08 TECU. Over the test period, the mean positioning errors of the single‐frequency precise point positioning corrected by IGSG, SGG Post‐GIM, SGG RT‐GIM, and Klobuchar model are 0.14, 0.19, 0.21, and 0.25 m in the horizontal direction, respectively, while the corresponding errors are 0.36, 0.33, 0.38, and 0.64 m in the up direction. Further, the mean biases of experimental days for the self‐consistency assessment are 0.06, −0.01, and −0.07 TECU for IGSG, SGG Post‐GIM, and SGG RT‐GIM, respectively. The corresponding RMS values are 1.19, 1.15, and 1.57 TECU.
... Meanwhile, Jason ionospheric data are independent of ground-based GNSS ionospheric data. Thus, ionospheric data can be employed to assess the accuracy of GIMs over oceanic regions (Li et al., 2018;Roma-Dollase et al., 2018). Jason-2 ionospheric data, that is, vertical total electron content (VTEC) data, can be derived from Jason-2 ionospheric range correction for Ku-band frequency using a smoothing window of 21 s (Imel, 1994). ...
The accuracy of ionospheric models estimated by ground‐based multiple global navigation satellite system ionospheric data over regions with sparse tracking stations is not ideal. To improve the accuracy of the estimated ionospheric model, different types of ionospheric data with different combinations were employed for previous studies. However, the ionospheric observational ranges for different types of ionospheric data are not the same. In this study, the accuracy of ionospheric maps generated by ground‐based ionospheric data (ground‐based strategy) and ground‐based ionospheric data combined with data provided by other geodetic measurements normalized by the single‐layer normalization method (multi‐source strategy) were studied. The results showed that the main differences between the ionospheric models estimated by the two strategies occur for data taken over the ocean, which mainly range from −1 to 0 total electron content unit (TECU). When assessed using Jason‐3 vertical total electron content data, the mean root mean square (RMS) value of the ionospheric model estimated by the multi‐source strategy was 5.03 TECU, which is approximately 15% smaller than that estimated by the ground‐based strategy. The maximum reduction in results using the multisource strategy was approximately 25% over different latitudes compared with that of the ground‐based strategy. Furthermore, the self‐consistency evaluation method was employed for evaluation. The results showed that the RMS of the ionospheric model estimated by the multi‐source strategy was 2.41 TECU, which is 3.60% better than that of the ground‐based strategy. The maximum reduction was 15% on different days.
... To provide comprehensive final GIM products, the IGS generates the final GIM with a weighted mean of some final GIM products from these IAACs [1,12]. Previous investigation illustrated that the IGSG is one of the highest precision final GIM products [12][13][14] and, thus, it is also used to validate the performance of different RT-GIM products. ...
In recent years, real-time global ionospheric map (RT-GIM) products have been actively developed by the international global navigation satellite system (GNSS) service (IGS) and its ionosphere associate analysis centers (IAACs) along with the increase of RT-GNSS multi-frequency and multi-constellation observations. In this study, the accuracy and consistency of three RT-GIM products from the Chinese Academy of Sciences (CAS), Wuhan University (WHU), and IGS are evaluated and analyzed utilizing three validation methods, namely, comparison with JASON-3 vertical total electron content (VTEC), the difference of slant total electron content (dSTEC), and IGS combined final GIM (IGSG) data. The test period was from 1 January 2019 to 31 December 2022, including the different solar activities. First, the comparison with JASON-3 data illustrates that the quality of the three RT-GIM products over oceans is in great consistency with that of the IGSG during different levels of solar activity and the daily mean bias (MEAN) values in low and high solar activities are approximately 5 and 10 TECU, respectively. The root mean square (RMS) values under low and high solar activities can be up to 7 and 12 TECU. Furthermore, the dSTEC validation results present that the MEAN values of RT-GIM products from different IAACs at high- and mid-latitude stations are about 0.5 TECU, which is smaller than those at low-latitude stations at about 1 TECU over continental regions. The standard deviation (STD) and RMS values for various RT-GIM products are within 3 and 4 TECU at low latitudes, respectively. In terms of the comparison with IGSG, the result shows that IGS combined RT-GIM (IRTG) presents better consistency than CAS RT-GIM (CRTG) and WHU RT-GIM (WRTG) in 2021 and 2022, with average annual STD and RMS values of 2.56 and 2.78 TECU, respectively. The daily biases of the RT-GIM products relative to IGSG can reach 4 TECU in high solar activities and the daily STD and RMS values are mainly within the 5 to 6 TECU range, respectively.
... Finally, the predicted and real-time products of the GIM constitute the essential tools for single-frequency precise point positioning (SF-PPP) applications where the accuracy of real-time GIM (RT-GIM) is estimated to be in the decimeter and meter levels in the horizontal and vertical directions. The predicted product is limited to be within 1-2 d because of the nonlinear variation in the ionosphere and the lack of real-time ionospheric observations [28][29][30]. Many recent studies for evaluating the accuracy of the RT-GIM are ongoing. ...
The demand for real-time high-precision positioning for global navigation satellite system applications is difficult to satisfy. In this regard, a single-frequency receiver is found to play an important role in overcoming this challenge, especially in developing countries where economic factors are a major restriction. Hence, the development of built-in models, such as the Klobuchar model, is an important objective for single-frequency users to mitigate the effect of ionospheric delay errors in real-time applications. Accordingly, this study aims to devise a new approach to enhance the behavior of the Klobuchar model and increase its efficiency in resolving the aforementioned problem. The new approach seeks to enhance the behavior of the Klobuchar model without refining or increasing its coefficients. To eliminate the ionospheric delay disturbance, the proposed methodology applies normalization and filtration processes to the raw ionospheric delay probability distribution estimated by the unified least squares technique. A final assessment of the new method for enhancing the Klobuchar behavior in predicting the precise position of a single-frequency static receiver under different weather conditions around the globe is presented in this paper.
... C1PG is the one-day TEC prediction provided by the Center for Orbit Determination in Europe (CODE). It has been reported that the global TEC map prediction accuracy of C1PG is higher than that of two other International Analysis Centers (IAACs), namely, the European Space Agency (ESA) and the University of Bern (UPG) [35]. ...
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.
... Each IGS analysis center delivers 1-and 2-day predicted ionosphere maps using different machine learning models (Li et al. 2018). For VTEC predictions, two main approaches are used: 3D forecast and 1D forecast. ...
Global navigation satellite system (GNSS) signals are significantly affected by the ionosphere. An efficient way to assess the ionospheric effects on GNSS signals is by retrieving the vertical total electron content (VTEC). Here, we propose convolutional recurrent neural network architectures to forecast VTEC based on global ionosphere maps (GIMs) of the days before the prediction period. We proposed modifications to the encoder–decoder convolutional long short-term memory (ED-ConvLSTM) architecture by innovatively using GIMs from several days and exploring the previous day’s GIM. Three new architectures were tested: The first one uses a residual connection to force the network to learn the difference between the previous and the next-day GIM; the second one uses the memory from the encoder to improve the transformation from the previous to the next-day GIM; and a third one uses 3 × 3 kernels on the encoder and 1 × 1 kernels on the decoder. Two experiments were performed using the international GNSS service (IGS) final GIM product from the years 2014–2015 (high solar activity) and 2019–2020 (low solar activity). The proposed architectures obtained better results than the original version of ED-ConvLSTM and other baseline models. We evaluated the influence of the number of GIMs (from one to four days) in the next-day GIM predictions. The results suggest that providing more than one day of GIM to the proposed networks can lead to better prediction metrics.
... A number of authors compared the ionospheric contribution from GNSS, VLBI, DORIS, radio occultation observations, and dual-band satellite altimeters (Sekido et al. 2003;Hobiger et al. 2006;Dettmering et al. 2011;Hernández-Pajares et al. 2017;Cokrlic et al. 2018;Li et al. 2018Li et al. , 2019Xiang & Gao 2019;Wielgosz et al. 2021;Zhao et al. 2021;Motlaghzadeh et al. 2022). A message these publications convey is there is a reasonable agreement between GNSS TEC maps and other techniques and there are no majors problems. ...
... Satellite altimetry using Jason satellites (Vaze et al. 2010, and references therein) provides an independent way for assessing the level of disagreement between direct vertical TEC measurements and GNSS TEC maps. Li et al. (2018) showed that comparisons of the differences revealed significant systematic biases that depend on geomagnetic latitude. However, an attempt to characterize these additive biases in terms of the rms was not very productive. ...
The ionospheric path delay impacts single-band, very long baseline interferometry (VLBI) group delays, which limits their applicability for absolute astrometry. I consider two important cases: when observations are made simultaneously in two bands, but delays in only one band are available for a subset of observations; and when observations are made in one-band design. I developed optimal procedures of data analysis for both cases using Global Navigation Satellite System (GNSS) ionosphere maps, provided a stochastic model that describes ionospheric errors, and evaluated their impact on source position estimates. I demonstrate that the stochastic model is accurate at a level of 15%. I found that using GNSS ionospheric maps as is introduces serious biases in estimates of declination and I developed a procedure that almost eliminates them. I found serendipitously that GNSS ionospheric maps have multiplicative errors and have to be scaled by 0.85 in order to mitigate the declination bias. A similar scale factor was found in comparison of the vertical total electron content from satellite altimetry against GNSS ionospheric maps. I favor interpretation of this scaling factor as a manifestation of the inadequacy of the thin-shell model of the ionosphere. I showed that we are able to model the ionospheric path delay to the extent that no noticeable systematic errors emerge and we are able to assess adequately the contribution of the ionosphere-driven random errors on source positions. This makes single-band absolute astrometry a viable option that can be used for source position determination.
... A-CHAIM also makes use of space-borne altimeter data from the JASON-3 satellite mission, provided by the NOAA National Oceanographic Data Center. As a by-product of the altimeter solution for sea-surface height, vertical ionospheric TEC above the ocean can be inferred (Li et al., 2018). This is done following the same concept as GNSS TEC products, where JASON's Ku band antenna excess phase can be directly related to the TEC along the ray path as ...
The Assimilative Canadian High Arctic Ionospheric Model (A‐CHAIM) is an operational ionospheric data assimilation model that provides a 3D representation of the high latitude ionosphere in Near‐Real‐Time (NRT). A‐CHAIM uses low‐latency observations of slant Total Electron Content (sTEC) from ground‐based Global Navigation Satellite System (GNSS) receivers, ionosondes, and vertical TEC from the JASON‐3 altimeter satellite to produce an updated electron density model above 45° geomagnetic latitude. A‐CHAIM is the first operational use of a particle filter data assimilation for space environment modeling, to account for the nonlinear nature of sTEC observations. The large number (>10⁴) of simultaneous observations creates significant problems with particle weight degeneracy, which is addressed by combining measurements to form new composite observables. The performance of A‐CHAIM is assessed by comparing the model outputs to unassimilated ionosonde observations, as well as to in‐situ electron density observations from the SWARM and DMSP satellites. During moderately disturbed conditions from 21 September 2021 through 29 September 2021, A‐CHAIM demonstrates a 40%–50% reduction in error relative to the background model in the F2‐layer critical frequency (foF2) at midlatitude and auroral reference stations, and little change at higher latitudes. The height of the F2‐layer (hmF2) shows a small 5%–15% improvement at all latitudes. In the topside, A‐CHAIM demonstrates a 15%–20% reduction in error for the Swarm satellites, and a 23%–28% reduction in error for the DMSP satellites. The reduction in error is distributed evenly over the assimilation region, including in data‐sparse regions.
... A number of authors compared the ionospheric contribution from GNSS, VLBI, DORIS, radio occultation observation, and dual-band satellite altimeters (Sekido et al. 2003;Hobiger et al. 2006;Dettmering et al. 2011;Hernández-Pajares et al. 2017;Cokrlic et al. 2018;Li et al. 2018Li et al. , 2019Xiang & Gao 2019;Wielgosz et al. 2021;Zhao et al. 2021;Motlaghzadeh et al. 2022). A message these publications convey is there is a reasonable agreement between GNSS TEC maps and other techniques and there are no majors problems. ...
... Satellite altimetry using Jason satellites (Vaze et al. 2010, and references therein) provides an independent way for assessment of a level of the disagreement between direct vertical TEC measurements and GNSS TEC maps. Li et al. (2018) showed that comparisons of the differences revealed significant systematic biases that depend on geomagnetic latitude. However, an attempt to characterize these additive biases in terms of Declination (deg) Figure 12. ...
The ionospheric path delay impacts single-band very long baseline interferometry (VLBI) group delays, which limits their applicability for absolute astrometry. I consider two important cases: when observations are made simultaneously at two bands, but delays at only one band are available for a subset of observations and when observations are made at one band only by design. I developed optimal procedures of data analysis for both cases using Global Navigation Satellite System (GNSS) ionosphere maps, provided a stochastic model that describes ionospheric errors, and evaluated their impact on source position estimates. I demonstrate that the stochastic model is accurate at a level of 15%. I found that using GNSS ionospheric maps as is introduces serious biases in estimates of declinations and I developed the procedure that almost eliminates them. I found serendipitously that GNSS ionospheric maps have multiplicative errors and have to be scaled by 0.85 in order to mitigate the declination bias. A similar scale factor was found in comparison of the vertical total electron contents from satellite altimetry against GNSS ionospheric maps. I favor interpretation of this scaling factor as a manifestation of the inadequacy of the thin shell model. I showed in this study that we are able to model the ionospheric path delay to the extent that no systematic errors emerge and we are able to adequately assess the contribution of the ionosphere-driven random errors on source positions. This makes single-band absolute astrometry a viable option that can be used for source position determination.
... The TEC maps predicted by our CAiTST model and 1-day CODE prediction model are named CTPG and C1PG, respectively. The C1PG has been proven to have better forecasting performance than E1PG and U2PG [37], which are predicted ionospheric products produced by the European Space Operations Center (ESOC) and UPC, respectively. In addition, the superiority of our CAiTST model is assessed by comparing the differences between CTPG and C1PG with respect to CODG. ...
In recent years, transformer has been widely used in natural language processing (NLP) and computer vision (CV). Comparatively, forecasting image time sequences using transformer has received less attention. In this paper, we propose the conv-attentional image time sequence transformer (CAiTST), a transformer-based image time sequences prediction model equipped with convolutional networks and an attentional mechanism. Specifically, we employ CAiTST to forecast the International GNSS Service (IGS) global total electron content (TEC) maps. The IGS TEC maps from 2005 to 2017 (except 2014) are divided into the training dataset (90% of total) and validation dataset (10% of total), and TEC maps in 2014 (high solar activity year) and 2018 (low solar activity year) are used to test the performance of CAiTST. The input of CAiTST is presented as one day’s 12 TEC maps (time resolution is 2 h), and the output is the next day’s 12 TEC maps. We compare the results of CAiTST with those of the 1-day Center for Orbit Determination in Europe (CODE) prediction model. The root mean square errors (RMSEs) from CAiTST with respect to the IGS TEC maps are 4.29 and 1.41 TECU in 2014 and 2018, respectively, while the RMSEs of the 1-day CODE prediction model are 4.71 and 1.57 TECU. The results illustrate CAiTST performs better than the 1-day CODE prediction model both in high and low solar activity years. The CAiTST model has less accuracy in the equatorial ionization anomaly (EIA) region but can roughly predict the features and locations of EIA. Additionally, due to the input only including past TEC maps, CAiTST performs poorly during magnetic storms. Our study shows that the transformer model and its unique attention mechanism are very suitable for images of a time sequence forecast, such as the prediction of ionospheric TEC map sequences.
