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Solar activity induces ionospheric irregularities that degrade Global Navigation Satellite System (GNSS) performance through amplitude and phase scintillation. Although numerous studies have investigated event‐driven or regional responses, the nonlinear coupling between solar radiation, ionospheric scintillation, and precise point positioning (PPP) degradation remains insufficiently quantified. This study presents a multi‐year observational analysis integrating GNSS measurements, ionospheric scintillation monitoring data, and solar activity indices from 2017 to 2024, covering high‐, mid‐, and low‐latitude regions. By jointly examining extreme ultraviolet (EUV) radiation, coronal mass ejection activity, scintillation indices (S4 and σφ${\\sigma }_{\\varphi }$ ), cycle‐slip occurrences, and PPP errors, a distinct nonlinear response of ionospheric scintillation to solar radiation is identified. Results reveal an approximately “inverted V‐shaped” dependence of scintillation intensity on EUV flux, with a critical threshold near 0.35 W/m2. In addition, enhanced solar radiation can suppress ionospheric scintillation, leading to transient improvements in positioning accuracy. On the day of peak solar flare activity, GNSS positioning accuracy exhibits a slight improvement as a result of reduced scintillation effects. Both scintillation occurrences and cycle slips aligned more closely with variations in EUV radiation flux. Results also indicate that low‐latitude regions exhibited a higher frequency of amplitude scintillation events (S4 > 0.2) than high‐latitude areas. The results refine the understanding of sun–ionosphere–positioning coupling and offer potential insights for assessing GNSS reliability and anti‐interference strategies during periods of elevated solar activity.

We propose a method for Global Ionospheric Maps of Total Electron Content forecasting using the Nearest Neighbour method. The assumption is that in a database of global ionosphere maps spanning more than two solar cycles, one can select a set of past observations that have similar geomagnetic conditions to those of the current map. The assumption is that the current ionospheric condition can be expressed by a linear combination of conditions seen in the past. The average of these maps leads to common geomagnetic components being preserved and those not shared by several maps being reduced. The method is based on searching the historical database for the dates of the maps closest to the current map and using as a prediction the maps in the database that correspond to time shifts on the prediction horizons. In contrast to other methods of machine learning, the implementation only requires a distance computation and does not need a previous step of model training and adjustment for each prediction horizon. It also provides confidence intervals for the forecast. The method has been analyzed for two full years (2015 and 2018), for selected days of 2015 and 2018, i.e., two storm days and two non-storm days and the performance of the system has been compared with CODE (24- and 48-h forecast horizons).

This study introduces a Bayesian probabilistic model for forecasting the fluctuations in the Rate of TEC Index (ROTI), which indicate the presence of ionospheric disturbances that can impact Global Navigation Satellite Systems (GNSS) and communication networks. The forecast method divides the Earth into a grid of 2 . 5 ∘ latitude by 5 ∘ longitude cells to predict when ROTI will exceed thresholds of 0.1, 0.25 and 0.5 TECU/min, with time horizons ranging from 30 min to 6 h. The method is based on the burstiness property of long-tailed distributions and provides as a forecast the median value of activity at each range, of both ROTI amplitude and forecast horizon. Previous proposed ROTI forecasting methods may degrade when faced with missing data points and the irregular, heavy-tailed characteristics of ROTI. In contrast, our model, based on the power-law dynamics observed in the persistent and bursty nature of long-tail distributions, allows for gaps in the measurements and provides a global forecast for regions covered by the network of GNSS stations. The performance of the model has been validated against historical GNSS data across various ionospheric conditions, demonstrating its robustness. The proposed Bayesian probabilistic model demonstrates robust forecasting capabilities, validated across diverse ionospheric conditions using historical GNSS data. It achieves strong performance metrics, with Weighted Kappa values exceeding 40% for prediction horizons up to 120 min and maintaining Mean Precision above 65% across all tested horizons from 30 min to 6 h. By forecasting the probability of ROTI exceeding specific levels, this method helps to identify geographical regions where GNSS reliability may be compromised, thereby aiding in the mitigation of adverse space weather effects on critical navigation and communication systems.

This paper compares the dimension reduction or feature extraction techniques, e.g., Principal Component Analysis, Factor Analysis, Independent Component Analysis and Neural Networks Principal Component Analysis, which are used as techniques for extracting the underlying systematic risk factors driving the returns on equities of the Mexican Stock Exchange, under a statistical approach to the Arbitrage Pricing Theory. We carry out our research according to two different perspectives. First, we evaluate them from a theoretical and matrix scope, making a parallelism among their particular mixing and demixing processes, as well as the attributes of the factors extracted by each method. Secondly, we accomplish an empirical study in order to measure the level of accuracy in the reconstruction of the original variables.

Swarm electron density (Ne) observations from the Langmuir probe (LP) can detect ionospheric disturbances at the altitude of a satellite. Along-track satellite observations provide a large number of very short observations of different places in the ionosphere, where Ne is disturbed. Moreover, different perturbations occupy various Ne signal frequencies. Therefore, such short signals are more recognizable in two dimensions, where aside from their change in time, we can observe their diversity in the frequency domain. Spectral analysis is an essential tool applied here, as it enables signal decomposition and the recognition of composite patterns of Ne disturbances that occupy different frequencies. This study shows a high-resolution application of short-term Fourier transform (STFT) to Swarm Ne observations in the Papua New Guinea region in the vicinity of earthquakes, tsunamis, and related general seismic activity. The system of tectonic plate junctions, including the Pacific–Australian boundary, is located orthogonally to Swarm track footprints. The selected wavelengths of seismically induced ionospheric disturbances detected via Swarm are compared with the three sets of three-month records of seismic activity: in the winter solstice of 2016/2017, when seismic activity was highest, and in the summer solstice and vernal equinox of 2016, which were calmer. Moreover, more Swarm data records are analyzed at the same latitudes for validation purposes, in a place where there are no tectonic plate boundaries that are orthogonal to the Swarm orbital footprint. Additional validation is supplied through Swarm Ne observations from completely different latitudes, where the Swarm orbital footprint orthogonally crosses a different subducting plate boundary. Aside from the seismic energy, the solar radio flux (F10.7), equatorial plasma bubbles (EPBs), and geomagnetic ap and Dst indices are also reviewed here. Their influence on the ionospheric Ne is also found in Swarm observations. Finally, the Pearson correlation coefficient (PCC), applied to the pairs of 3-month time series created from Swarm Ne variations, seismic energy, ap, Dst, and F10.7, summarizes the graphical inspection of mutual correlations. It points to the predominant correlation of Swarm Ne disturbances with seismicity, especially during nighttime. We show that most of the Ne disturbances at a selected wavelength of 300 km correlate more with seismicity than with geomagnetic and solar indices. Therefore, Swarm LP can be assessed as being capable of observing the lithosphere–atmosphere–ionosphere coupling (LAIC) from the orbit.

This paper presents a new way of combining Abel inversion and the Chapman model with a linearly increasing scale height to retrieve ionospheric electron density vertical profiles from truncated-sounding radio-occultation data. A linear Vary–Chap model is used to cover the blind region due to data truncation, with parameters estimated by enumeration of the possible values in a grid centered around a set of parameters compatible with ionospheric physics. The resulting electron density is estimated with its corresponding error from the linear least-squares solution presenting the smaller post-fit residual on the input GNSS carrier-phase measurements. The results, tested on a set of representative GNSS RO measurements obtained by COSMIC/FORMOSAT-3, show that this method can retrieve EDVPs with a predominant absolute and relative error of 1010e−m−3 and 5%, respectively, and in less than 10 s per profile, which makes this method suitable for near real-time applications in upcoming missions such as EUMETSAT Polar System-Second Generation.

This paper compares the dimension reduction or feature extraction techniques, e.g., Principal Component Analysis, Factor Analysis, Independent Component Analysis and Neural Networks Principal Component Analysis, which are used as techniques for extracting the underlying systematic risk factors driving the returns on equities of the Mexican Stock Exchange, under a statistical approach to the Arbitrage Pricing Theory. We carry out our research according to two different perspectives. First, we evaluate them from a theoretical and matrix scope, making a parallelism among their particular mixing and demixing processes, as well as the attributes of the factors extracted by each method. Secondly, we accomplish an empirical study in order to measure the level of accuracy in the reconstruction of the original variables.

The time evolution of the total number of free electrons in the Earth’s ionosphere, i.e., the Global Electron Content (GEC), during more than two solar cycles is analyzed in this work. The GEC time series has been extracted from the Global Ionospheric Maps (GIMs) of Vertical Total Electron Content (VTEC) estimated by UPC-IonSAT with TOMION-v1 software from global GPS measurements since the end of 1996. A dual-layer voxel-based tomographic model solved with a forward Kalman scalar filter, from dual-frequency carrier GPS data only, provides the so-called UQRG GIM after VTEC kriging interpolation, with a resolution of 15 min in time, 5° in longitude and 2.5° in latitude. UQRG is one of the best behaving GIMs in the International GNSS Service (IGS).In this context, the potential application of the GEC spectrum evolution as a potential space weather index is discussed and demonstrated.

The Real-Time Working Group (RTWG) of the International GNSS Service (IGS) is dedicated to providing high-quality data and high-accuracy products for Global Navigation Satellite System (GNSS) positioning, navigation, timing and Earth observations. As one part of real-time products, the IGS combined Real-Time Global Ionosphere Map (RT-GIM) has been generated by the real-time weighting of the RT-GIMs from IGS real-time ionosphere centers including the Chinese Academy of Sciences (CAS), Centre National d'Etudes Spatiales (CNES), Universitat Politècnica de Catalunya (UPC) and Wuhan University (WHU). The performance of global vertical total electron content (VTEC) representation in all of the RT-GIMs has been assessed by VTEC from Jason-3 altimeter for 3 months over oceans and dSTEC-GPS technique with 2 d observations over continental regions. According to the Jason-3 VTEC and dSTEC-GPS assessment, the real-time weighting technique is sensitive to the accuracy of RT-GIMs. Compared with the performance of post-processed rapid global ionosphere maps (GIMs) and IGS combined final GIM (igsg) during the testing period, the accuracy of UPC RT-GIM (after the improvement of the interpolation technique) and IGS combined RT-GIM (IRTG) is equivalent to the rapid GIMs and reaches around 2.7 and 3.0 TECU (TEC unit, 1016 el m−2) over oceans and continental regions, respectively. The accuracy of CAS RT-GIM and CNES RT-GIM is slightly worse than the rapid GIMs, while WHU RT-GIM requires a further upgrade to obtain similar performance. In addition, a strong response to the recent geomagnetic storms has been found in the global electron content (GEC) of IGS RT-GIMs (especially UPC RT-GIM and IGS combined RT-GIM). The IGS RT-GIMs turn out to be reliable sources of real-time global VTEC information and have great potential for real-time applications including range error correction for transionospheric radio signals, the monitoring of space weather, and detection of natural hazards on a global scale. All the IGS combined RT-GIMs generated and analyzed during the testing period are available at https://doi.org/10.5281/zenodo.5042622 (Liu et al., 2021b).

In this paper, we propose a method for the generation of real-time global ionospheric map (RT-GIM) of vertical total electron content (VTEC) from GNSS measurements. The need for interpolation arises from the fact that the ionospheric pierce point (IPP) measurements from satellites to stations are not distributed uniformly over the ionosphere, leaving unfilled gaps at oceans or poles. The method we propose is based on using a high-quality historical database of post-processed GIMs that comprises more than two solar cycles, calculates the GIM by weighted superposition on a subset of the database with the compatible solar condition. The linear combination of GIMs in the database was obtained by minimizing a ℓ 2 distance between VTEC measurements at the IPPs and the VTECs from the database, adding a ℓ 1 penalization on the weights to assure a sparse solution. The process uses a Sun-fixed geomagnetic reference frame. This method uses the atomic decomposition/least absolute shrinkage and selection operator (LASSO), which will be denoted as atomic decomposition interpolator of GIMs (ADIGIM). As the computation is done in milliseconds, the interpolation is performed in real time. In this work, two products were developed, denoted as UADG and UARG, the UADG in real time and UARG with a latency of 24 h to benefit from the availability of a greater number of stations. The altimeter JASON3 VTEC measurements were used as reference. The quality of interpolated RT-GIMs from day 258 of 2019 to 155 of the year 2020 is compared with other RT/non-RT GIM products such as those from International GNSS Service (IGS), Centre National d’Etudes Spatiales (CNES), Chinese Academy of Sciences (CAS), Polytechnic University of Catalonia (UPC) and others. The RT ADIGIM performance proved to be better, nearly as good as the rapid or final GIMs computed retrospectively with delays of hours to days. Besides, the non-RT ADIGIM quality is as good or better than most GIM products. The oceanic regions have been included in the assessment which showed that ADIGIM interpolation gives the best estimation (referred to JASON3). The developed method, UADG, will constitute the next-generation UPC RT-GIM, and also UARG will improve the current product UQRG (the current UPC rapid GIM product computed retrospectively) due to its complementary information.