Regional Vertical Total Electron Content Research Articles

Regional ionospheric electron density modeling by assimilation of GPS-derived TEC into IRI-provided grids on May 8, 2016

Retrieved vertical total electron content (VTEC) via dual-frequency GPS measurements is a valuable observation for regional VTEC modeling of the ionosphere (3D), and also ionospheric electron density (IED) modeling (4D). In the case of 4D modeling, spatial and temporal changes in IED are imaged. 4D reconstruction of IED in different ionosphere layers is not possible only by retrieved VTECs. In all IED modeling methods, in addition to VTEC observations, a priori knowledge of how electron density is distributed in different layers is required, which is often taken from global empirical models. One of these methods is data assimilation, in which the information of a global model is considered as background and both observations and background are used optimally for IED modeling. Data assimilation has more prominent importance in regions where the observations are sparse. In this study, a grid-based data assimilation method is proposed for IED modeling. The optimum interpolation method (OI) is presented with a modification to find the optimal variance factor related to the background covariance matrix. The covariance matrix of the background during the data assimilation interval is estimated by an optimization process. The method is utilized for regional assimilative IED modeling over Iran with sparse VTEC data from a low number of permanent GPS stations on May 8, 2016 which is the most active ionospheric day in that year. International reference ionosphere (IRI) is considered as background, and although it has a significant bias in the study region, the proposed method resulted in an accurate regional IED model. The model is evaluated in two ways. First, by measuring RMS of the differences between parts of VTECs that are excluded from observations as test data and the obtained VTECs from the model. Second, by examining the accuracy of ionospheric delay estimation via single-frequency positioning at a control station in Tehran. Despite the use of sparse data on an active ionospheric day and poor background accuracy in the study region, the constructed regional assimilative model is accurate both in RMS with test data and ionospheric delay estimation.

SHAKING: Adjusted spherical harmonics adding KrigING method for near real-time ionospheric modeling with multi-GNSS observations

Precise positioning based on Global Navigation Satellite System (GNSS) technique requires high accuracy ionospheric total electron content (TEC) correction models to account for the ionospheric path delay errors. We present an adjusted Spherical Harmonics Adding KrigING method (SHAKING) approach for regional ionospheric vertical TEC (VTEC) modeling in real time. In the proposed SHAKING method, the VTEC information over the sparse observation data area is extrapolated by the Adjusted Spherical Harmonic (ASH) function, and the boundary distortion in regional VTEC modeling is corrected by the stochastic VTEC estimated using Kriging interpolation. Using real-time GPS, GLONASS and BDS-2/3 data streams of the Crust Movement Observation Network of China (CMONOC), the SHAKING-based regional ionospheric VTEC maps are re-constructed over China and its boundary regions. Compared to GNSS VTECs derived from the independent stations, the quality of SHAKING solution improves by 13–31% and 6–33% with respect to the ASH-only solution during high and low geomagnetic periods, respectively. Compared to the inverse distance weighting (IDW) generated result, significant quality improved of SHAKING-based VTEC maps is also observed, especially over the edge areas with an improvement of 60–80%. Overall, the proposed SHAKING method exhibits notable advantage over the existing regional VTEC modeling techniques, which can be used for regional TEC modeling and associated high-precision positioning applications.

Improving the performance of time varying spherical radial basis functions in regional VTEC modeling with sparse data

Least-squares parameterization of retrieved Vertical Total Electron Content (VTEC) from permanent dual-frequency GPS stations in terms of Time Varying Spherical Radial Basis Functions (TV-SRBFs) with optimal shape parameter leads to proper regional VTEC reconstruction at Ionospheric Pierce Points (IPPs). However, in the area where there is no observation, the modeling result is not satisfactory. This feature is especially tangible when the number of IPPs in the study area is low with poor geometric distribution, which leads to a rank deficient problem. Whereas, if the global ionospheric maps (GIMs) are used as a background in estimating the optimal shape parameter of TV-SRBFs and coefficients of the expansion, the stated obstacle to produce accurate regional ionospheric maps will be removed. For this purpose, an objective function is defined and optimized. The objective function consists of three terms. First, L-2 norm of the differences between the reproduced VTECs and values obtained from the receivers’ observations. Second, L-2 norm of the differences between the reproduced values on a regular grid with the values obtained from the spatial interpolation of GIM at a specific moment in the modeling interval. Third, the discrete smoothing norm of the coefficients of TV-SRBFs. Since the obtained VTECs from GPS receivers are more accurate than the resulted VTECs from interpolation of GIMs and also a regularization parameter is needed due to the ill-posedness, the three objectives cannot be considered with the same weights in the multi-objective optimization. Hence the weighted sum method with the preference-based solution is applied to obtain the optimal relative weight of GIMs, the regularization parameter and the coefficients. Moreover, utilizing the least-squares collocation (LSC) can also improve the modeling accuracy to some extent. The proposed method is applied for hourly regional VTEC modeling over Iran from 3 May to 9 May 2016, which had both low and very high geomagnetic activities. A portion of the retrieved VTECs which is excluded from the modeling dataset, is considered as test data. The Root Mean Square (RMS) of the differences between obtained VTECs from regional constructed model and test data is 0.94 TECU in the study period. RMS of the differences between obtained VTECs from the regional model and VTECs of two control stations which are not involved in the modeling are 1.12 TECU and 1.24 TECU. Also, the regional model performs well in ionospheric delay estimation and the accuracy of single-frequency positioning at control stations in the study period is better than 0.7 m.

Regional application of C1 finite element interpolation method in modeling of ionosphere total electron content over Europe

• A novel approach for regional ionosphere grid model with high spatial-temporal resolution is suggested. • The results of the new model is analyzed at different disturb geomagnetic and solar conditions. • A comparative analysis between the results of new model, GIM, NeQuick and GPS-TEC is made. In this paper, a novel approach based on C 1 finite element (FE) interpolation is used to construct a regional ionospheric grid model (RIGM) with high spatio-temporal resolution over Europe. The spatial resolution of the new model is 0.5 0 for a longitude and latitude and a temporal resolution is 15 min. Observations of 38 GPS stations at different days and seasons with different geomagnetic and solar activity conditions are used to evaluate the new method. All stations are used to discretize the whole domain of the problem into separate triangular patches using a Delaunay triangulation algorithm. In this case, GPS stations would be the vertices of the triangular patches. Also, the position of stations in sun-fixed coordinate system with coordinates of latitude and longitude are chosen in order to consider the temporal variations of vertical total electron content (VTEC). To model the behavior of VTEC in each triangular patch, a particular shape function is defined which is fitted to VTEC values at three vertices of each triangle while it satisfies C 1 continuity of VTEC at the common edges of the adjacent triangles. The results of the new model are compared with the VTEC of GPS at 4 control stations as well as global ionosphere map (GIM) and NeQuick models. Statistical parameters, including correlation coefficient, root mean square error (RMSE), standard deviation and dVTEC = |VTEC GPS - VTEC model | have been used to evaluate the error of the models. In low geomagnetic activity (KP < 4), the average RMSE at 4 control stations for FE, GIM and NeQuick models are 0.89, 1.05 and 6.42 TECU, respectively, while in the high geomagnetic activity (KP > 4), they are 1.24, 1.68 and 7.62 TECU, respectively. For further analysis, the accuracy of three models in precise point positioning (PPP) has been also evaluated. In PPP method, there is an improvement of about 1–16 mm compared to GIM and NeQuick models at coordinate components of control stations in high geomagnetic activity. The results of the analysis performed in this paper show that the FE model has a very high capability and accuracy in regional VTEC modeling in high and low geomagnetic conditions. The regional accuracy of this model is higher than GIM and NeQuick models and therefore can be considered as a new model for the ionosphere.

Regional Assimilation of GPS-Derived TEC into GIMs

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.

Higher order ionospheric delay and derivation of regional total electron content over Ethiopian global positioning system stations

The Global Positioning System (GPS) is a space-based radio positioning system which is capable of providing continuous position, velocity and time information to users anywhere on, or near, the surface of the Earth. The positional accuracy of GPS is limited by several sources of error, such as satellite and receiver clock offsets, signal propagation delays (due to the ionosphere and troposphere), multipath, receiver measurement noise, and instrument bias. The ionospheric delay is the predominant error source. The main objective of this work was to estimate the regional vertical Total Electron Content (vTEC) densities, using a linear combination of L1 and L2 carrier phase for higher order time delays at different thin-shell layers of the ionosphere (i.e. 60 km, 90 km, 150 km, 200 km and 450 km) over GPS stations in Ethiopia. Due to the high equatorial ionization anomaly and irregularity of the electron density distribution, we selected four GPS stations across the country. We studied longitudinal, latitudinal, and altitudinal variations in the ionosphere using GPS observables extracted by precise geodetic GAMIT-GLOBK software package. We obtained data from the 2013 to 2015 period for all stations. For daily data processing in GAMIT, we switched the International Geomagnetic Reference Field 2012 (IGRF-12) model (which consists of spherical harmonic coefficients) on and off, representing the Earth’s main field and its secular variation and ionospheric electron content along the signal path (available from the Centre for Orbit Determination in Europe (CODE)).Our results confirmed that there is latitudinal, longitudinal and altitudinal variation in the ionosphere. The density of total electron content and GPS positional error due to higher-order time delays have a positive correlation (more than 95%). The positional error, due to the higher order ionospheric delay, exceeds 4 mm for all GPS stations and reached up to 8 mm. Finally, we observed that the time delay due to the higher-order ionospheric effect in the L2 signal is twice that in the L1.We conclude that the GPS signal is affected by the higher order ionospheric delay by up to several centimetres due to its electron content and the Earth’s magnetic field.

Global and Regional High-Resolution VTEC Modelling Using a Two-Step B-Spline Approach

The ionosphere is one of the largest error sources in GNSS (Global Navigation Satellite Systems) applications and can cause up to several meters of error in positioning. Especially for single-frequency users, who cannot correct the ionospheric delay, the information about the state of the ionosphere is mandatory. Dual- and multi-frequency GNSS users, on the other hand, can correct the ionospheric effect on their observations by linear combination. However, real-time applications such as autonomous driving or precision farming, require external high accuracy corrections for fast convergence. Mostly, this external information is given in terms of grids or coefficients of the vertical total electron content (VTEC). Globally distributed GNSS stations of different networks, such as the network of the International GNSS Services (IGS), provide a large number of multi-frequency observations which can be used to determine the state of the ionosphere. These data are used to generate Global Ionosphere Maps (GIM). Due to the inhomogeneous global distribution of GNSS real-time stations and especially due to the large data gaps over oceanic areas, the global VTEC models are usually limited in their spatial and spectral resolution. Most of the GIMs are mathematically based on globally defined radial basis functions, i.e., spherical harmonics (SH), with a maximum degree of 15 and provided with a spatial resolution of 2.5 ° × 5 ° in latitude and longitude, respectively. Regional GNSS networks, however, offer dense clusters of observations, which can be used to generate regional VTEC solutions with a higher spectral resolution. In this study, we introduce a two-step model (TSM) comprising a global model as the first step and a regional model as the second step. We apply polynomial and trigonometric B-spline functions to represent the global VTEC. Polynomial B-splines are used for modelling the finer structures of VTEC within selected regions, i.e., the densification areas. The TSM provides both, a global and a regional VTEC map at the same time. In order to study the performance, we apply the developed approach to hourly data of the global IGS network as well as the EUREF network of the European region for St. Patrick storm in March 2015. For the assessment of the generated maps, we use the dSTEC analysis and compare both maps with different global and regional products from the IGS Ionosphere Associated Analysis Centers, e.g., the global product from CODE (Berne, Switzerland) and from UPC (Barcelona, Spain), as well as the regional maps from ROB (Brussels, Belgium). The assessment shows a significant improvement of the regional VTEC representation in the form of the generated TSM maps. Among all other products used for comparison, the developed regional one is of the highest accuracy within the selected time span. Since the numerical tests are performed using hourly data with a latency of one to two hours, the presented procedure is seen as an intermediate step for the generation of high precision regional real-time corrections for modern applications.

A New Ionospheric Model for Single Frequency GNSS User Applications Using Klobuchar Model Driven by Auto Regressive Moving Average (SAKARMA) Method Over Indian Region

The single-frequency users of Global Navigation Satellite System (GNSS) require an effective mathematical model that mitigate the dominant errors due to ionospheric delays. Klobuchar model approximately reduces ionospheric effect up to 50% through its coefficients in the navigation message, which is not sufficient for the GNSS single frequency users at critical applications. Hence, a new model, for Single Frequency GNSS User Applications using Klobuchar model driven by Auto Regressive Moving Average Method (SAKARMA) is proposed to forecast and enhance the precision of ionospheric delay estimations for GNSS users. The hourly VTEC maps are obtained from the Assimilated Indian Regional Vertical Total Electron Content (AIRAVAT) by the process of data assimilation using the Kalman filter exclusively for the Indian region (longitude: 65°E to 100°E; latitude: 5°N to 40°N) using 26 GPS TEC stations over Indian region. The accuracy of the SAKARMA model is investigated using the AIRAVAT maps for various Indian geographic regions during both geomagnetic quiet and disturbed conditions of September month in 2016 year. Furthermore, in order to test SAKARMA model, a dual-frequency Navigation with Indian Constellation (NavIC) receiver located at the KL Education Foundation, Guntur, India (geographic: 16.37°N, 80.37°E; geomagnetic: 7.44°N, 153.75°E) is used to collect the observations during 2 - 12 September 2017. Furthermore, SAKARMA model is also validated with Klobuchar model, Klobuchar-style coefficients provided by the Center for Orbit Determination in Europe (CODE) (CODKlob) Model, BeiDou System (BDS2) Model and NeQuick 2 Model over a low latitude NavIC station in forecasting the ionospheric delays. The experimental results of SAKARMA for NavIC have revealed that the MAPE for proposed SAKARMA model is 9-17% (accuracy: 83-91%), while 34-53% (accuracy: 47-66%) for the Klobuchar model. Thus, the results illustrate that the proposed SAKARMA model is capable of predicting the ionospheric delays for single frequency GNSS/NavIC users.

Generation of Assimilated Indian Regional Vertical TEC Maps

Regional ionospheric total electron content maps have become a prominent tool for understanding the dynamic behavior of the ionosphere. In recent times, ionospheric data assimilation methods have enhanced the prediction capabilities of global ionospheric models by embedding several standalone ionospheric remote sensing observations. In this study, an attempt is made to generate hourly Assimilated Indian Regional Vertical Total Electron Content (AIRAVAT) Maps by the process of data assimilation using the Kalman filter exclusively for the Indian region (longitude: 65° to 100°; latitude: 5° to 40°). Observations from the ground-based Global Positioning System aided Geo-Stationary Orbit Augmented Network and radio occultations from the space-based Constellation Observing System for Meteorology, Ionosphere, and Climate are introduced into the global ionospheric map developed by the Centre for Orbit Determination in Europe with a temporal resolution of 1 h. The AIRAVAT maps are created for a day of quiet (September 16, 2016) and disturbed (October 25, 2016) geomagnetic conditions. A new methodology is provided for the covariance matrix of initial background model errors through multivariate principal component analysis of solar and geomagnetic parameters. The equatorial ionization anomaly features are clearly captured in the developed AIRAVAT maps by using both the updated and forecasted steps of the Kalman filter. The AIRAVAT model is validated with an independent GNSS receiver through root-mean-square error analysis for both quiet and disturbed geomagnetic conditions to showcase the efficiency of the model. The quiet day RMSEs between the estimated TEC of proposed AIRAVAT model and the true data are approximately 2 TECU and 2.66 TECU for a disturbed day, respectively. The proposed AIRAVAT maps are useful for monitoring the impact of ionospheric space weather on satellite-based navigation and communication systems.

Near-real-time VTEC maps: New contribution for Latin America Space Weather

The development of regional services able to provide ionospheric vertical total electron content (VTEC) maps and ionospheric indexes with a high spatial resolution, and in near-real-time, are of great importance for both civilian applications and the research community. We provide here the methodologies, and an assessment, of such a system. It relies on the public Global Navigational Satellite Systems (GNSS) infrastructure in South America, incorporates data from multiple constellations (currently GPS, GLONASS, Galileo and BeiDou), employs multiple frequencies, and produces continental wide VTEC maps with a latency of just a few minutes. To assess the ability of our system to model the ionospheric behavior we performed a year-round intercomparison between our near-real-time regional VTEC maps, and VTEC maps of verified quality produced by several referent analysis centers, resulting in mean biases lower than 1 TEC units (TECU). Also, the evaluation of our products against direct and independent GNSS-based slant TEC measurements shows RMS values better than 1 TECU. In turn, ionospheric weather W-index maps were generated, for calm and disturbed geomagnetic scenarios, solely employing our quality verified VTEC maps. The spatial representation of these W-index maps reflects the state of the ionosphere, with a resolution of 0.5×0.5 degrees. Finally, we conclude that our products, computed every 15 min, do provide an excellent spatial representation of the regional TEC, and are able to provide the bases for the possible computation of ionospheric W-index maps, also in near-real-time.

Real-Time Precise Point Positioning (RTPPP) with raw observations and its application in real-time regional ionospheric VTEC modeling

Precise Point Positioning (PPP) is an absolute positioning technology mainly used in post data processing. With the continuously increasing demand for real-time high-precision applications in positioning, timing, retrieval of atmospheric parameters, etc., Real-Time PPP (RTPPP) and its applications have drawn more and more research attention in recent years. This study focuses on the models, algorithms and ionospheric applications of RTPPP on the basis of raw observations, in which high-precision slant ionospheric delays are estimated among others in real time. For this purpose, a robust processing strategy for multi-station RTPPP with raw observations has been proposed and realized, in which real-time data streams and State-Space-Representative (SSR) satellite orbit and clock corrections are used. With the RTPPP-derived slant ionospheric delays from a regional network, a real-time regional ionospheric Vertical Total Electron Content (VTEC) modeling method is proposed based on Adjusted Spherical Harmonic Functions and a Moving-Window Filter. SSR satellite orbit and clock corrections from different IGS analysis centers are evaluated. Ten globally distributed real-time stations are used to evaluate the positioning performances of the proposed RTPPP algorithms in both static and kinematic modes. RMS values of positioning errors in static/kinematic mode are 5.2/15.5, 4.7/17.4 and 12.8/46.6 mm, for north, east and up components, respectively. Real-time slant ionospheric delays from RTPPP are compared with those from the traditional Carrier-to-Code Leveling (CCL) method, in terms of function model, formal precision and between-receiver differences of short baseline. Results show that slant ionospheric delays from RTPPP are more precise and have a much better convergence performance than those from the CCL method in real-time processing. 30 real-time stations from the Asia-Pacific Reference Frame network are used to model the ionospheric VTECs over Australia in real time, with slant ionospheric delays from both RTPPP and CCL methods for comparison. RMS of the VTEC differences between RTPPP/CCL method and CODE final products is 0.91/1.09 TECU, and RMS of the VTEC differences between RTPPP and CCL methods is 0.67 TECU. Slant Total Electron Contents retrieved from different VTEC models are also validated with epoch-differenced Geometry-Free combinations of dual-frequency phase observations, and mean RMS values are 2.14, 2.33 and 2.07 TECU for RTPPP method, CCL method and CODE final products, respectively. This shows the superiority of RTPPP-derived slant ionospheric delays in real-time ionospheric VTEC modeling.

Regional vertical total electron content (VTEC) modeling together with satellite and receiver differential code biases (DCBs) using semi-parametric multivariate adaptive regression B-splines (SP-BMARS)

There are various global and regional methods that have been proposed for the modeling of ionospheric vertical total electron content (VTEC). Global distribution of VTEC is usually modeled by spherical harmonic expansions, while tensor products of compactly supported univariate B-splines can be used for regional modeling. In these empirical parametric models, the coefficients of the basis functions as well as differential code biases (DCBs) of satellites and receivers can be treated as unknown parameters which can be estimated from geometry-free linear combinations of global positioning system observables. In this work we propose a new semi-parametric multivariate adaptive regression B-splines (SP-BMARS) method for the regional modeling of VTEC together with satellite and receiver DCBs, where the parametric part of the model is related to the DCBs as fixed parameters and the non-parametric part adaptively models the spatio-temporal distribution of VTEC. The latter is based on multivariate adaptive regression B-splines which is a non-parametric modeling technique making use of compactly supported B-spline basis functions that are generated from the observations automatically. This algorithm takes advantage of an adaptive scale-by-scale model building strategy that searches for best-fitting B-splines to the data at each scale. The VTEC maps generated from the proposed method are compared numerically and visually with the global ionosphere maps (GIMs) which are provided by the Center for Orbit Determination in Europe (CODE). The VTEC values from SP-BMARS and CODE GIMs are also compared with VTEC values obtained through calibration using local ionospheric model. The estimated satellite and receiver DCBs from the SP-BMARS model are compared with the CODE distributed DCBs. The results show that the SP-BMARS algorithm can be used to estimate satellite and receiver DCBs while adaptively and flexibly modeling the daily regional VTEC.

Carrier-phase two-way satellite frequency transfer over a very long baseline

In this paper we report that carrier-phase two-way satellite time and frequency transfer (TWSTFT) was successfully demonstrated over a very long baseline of 9000 km, established between the National Institute of Information and Communications Technology (NICT) and the Physikalisch-Technische Bundesanstalt (PTB). We verified that the carrier-phase TWSTFT (TWCP) result agreed with those obtained by conventional TWSTFT and GPS carrier-phase (GPSCP) techniques. Moreover, a much improved short-term instability for frequency transfer of 2 × 10−13 at 1 s was achieved, which is at the same level as previously confirmed over a shorter baseline within Japan. The precision achieved was so high that the effects of ionospheric delay became significant; they are ignored in conventional TWSTFT even over a long link. We compensated for these effects using ionospheric delays computed from regional vertical total electron content maps. The agreement between the TWCP and GPSCP results was improved because of this compensation.

Regional ionosphere modeling in support of IRI and wavelet using GPS observations

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.

Non-parametric regional VTEC modeling with Multivariate Adaptive Regression B-Splines

In this work Multivariate Adaptive Regression B-Splines (BMARS) is applied to regional spatio-temporal mapping of the Vertical Total Electron Content (VTEC) using ground based Global Positioning System (GPS) observations. BMARS is a non-parametric regression technique that utilizes compactly supported tensor product B-splines as basis functions, which are automatically obtained from the observations. The algorithm uses a scale-by-scale model building strategy that searches for B-splines at each scale fitting adequately to the data and provides smoother approximations than the original Multivariate Adaptive Regression Splines (MARS). It is capable to process high dimensional problems with large amounts of data and can easily be parallelized. The real test data is collected from 32 ground based GPS stations located in North America. The results are compared numerically and visually with both the regional VTEC modeling generated via original MARS using piecewise-linear basis functions and another regional VTEC modeling based on B-splines.

Testing regional vertical total electron content maps over Europe during the 17–21 January 2005 sudden space weather event

The intense level of solar activity recorded from 16 to 23 January 2005 led to a series of events with different signatures at the Earth's ionospheric distances. Measurements of the critical frequency of the F2 layer foF2 and the vertical total electron content (VTEC) are used to describe the temporal and spatial electron density distributions during this space weather event, which gives an excellent opportunity to test regional VTEC maps over Europe under such disturbed solar‐terrestrial conditions. In this context, the tests used to validate the International GNSS Service (IGS) VTEC maps have been applied to assess the accuracy of the European Rutherford Appleton Laboratory (RAL) VTEC maps. Thus the self‐consistency test and the Jason altimeter test have been used to compare such performances with the IGS and Universitat Politecnica de Catalunya global ionospheric maps. The results show discrepancies between the RAL maps and the IGS ones, which leads to significant RMS and bias values of several total electron content units. Moreover, in this work a kriging technique to improve the accuracy of any regional VTEC map is also considered, with relative improvements of the RAL VTEC maps up to more than 20% at the peak of the storm.

A neural network approach for regional vertical total electron content modelling

A Neural Network model has been developed for estim ating the total electron content (TEC) of the ionosphere. TEC is proportional to the delay suffered by electromagnetic signals crossing the ionosphere and is among the er rors that impact GNSS (Global Navigation Satellite Systems) observations. Ionosph eric delay is particularly a problem for single frequency receivers, which cannot elimin ate the (first-order) ionospheric delay by combining observations at two frequencies. Singl e frequency users rely on applying corrections based on prediction models or on region al models formed based on actual data collected by a network of receivers. A regiona l model based on a neural network has been designed and tested using data sets collected by the Brazilian GPS Network (RMBC) covering periods of low and high solar activity. An alysis of the results indicates that the model is capable of recovering, on average, 85% of TEC values. K e y w o r d s : total electron content, ionosphere, regi onal ionospheric model, neural network