ALBERT

Description: Over the last 20 years, a large number of instruments have provided plasma density measurements in Earth's topside ionosphere. To utilize all of the collected observations for empirical modeling, it is necessary to ensure that they do not exhibit systematic differences and are adjusted to the same reference frame. In this study, we compare satellite plasma density observations from Gravity Recovery and Climate Experiment (GRACE), Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC), CHAllenging Minisatellite Payload (CHAMP), Swarm, and Communications/Navigation Outage Forecasting System (C/NOFS) missions. Electron densities retrieved from GRACE K‐Band Ranging (KBR) system, previously shown to be in excellent agreement with incoherent scatter radar (ISR) measurements, are used as a reference. We find that COSMIC radio occultation (RO) densities are highly consistent with GRACE‐KBR observations showing a mean relative difference of 〈2%, and therefore no calibration factors between them are necessary. We utilize the outstanding three‐dimensional coverage of the topside ionosphere by the COSMIC mission to perform conjunction analysis with in situ density observations from CHAMP, C/NOFS, and Swarm missions. CHAMP measurements are lower than COSMIC by ∼11%. Swarm densities are generally lower at daytime and higher at nighttime compared to COSMIC. C/NOFS ion densities agree well with COSMIC, with a relative bias of ∼7%. The resulting cross‐calibration factors, derived from the probability distribution functions, help to eliminate the systematic leveling differences between the data sets, and allow using these data jointly in a large number of ionospheric applications.

Description: Key Points: A systematic comparison of the plasma density data from CHAMP, C/NOFS, GRACE, COSMIC, and Swarm missions is performed. Electron densities retrieved from COSMIC‐RO agree well with GRACE‐KBR observations showing a relative difference of less than 2%. Intercalibration factors, allowing to eliminate the systematic offsets between the considered data sets, are presented.

Description: Helmholtz Pilot Projects Information & Data Science II, MAchine learning based Plasma density model project

Description: National Center for Atmospheric Research http://dx.doi.org/10.13039/100005323

Description: Air Force Office of Scientific Research http://dx.doi.org/10.13039/100000181

Description: National Science Foundation http://dx.doi.org/10.13039/100000001

Description: Monitoring the Vertical Total Electron Content (VTEC) of the ionosphere is important for applications ranging from navigation to detection of space weather events. Therefore, emerging efforts have been made by several analysis centers to estimate the VTEC using different approaches in real‐time. Global Navigation Satellite Systems (GNSS) is a crucial technology for ionosphere modeling due to its worldwide distributed receivers, high temporal resolution, and low latency data dissemination capability. The selection of a convenient approach to extract ionosphere information from GNSS and the representation of VTEC by an appropriate mathematical model are essential factors for providing fast and accurate ionosphere products. Contrarily to the widespread phase‐leveling method, which uses noisy and erroneous code measurements, the modeling concept in this paper utilizes pure carrier‐phase measurements. Measurements acquired through the International GNSS Service (IGS) real‐time service in Radio Technical Commission for Maritime Services format are from GPS, GLONASS, and GALILEO. The measurement biases, including the ambiguity of carrier‐phase measurements, are simultaneously estimated along with VTEC model parameters. In our approach, VTEC is represented by B‐spline expansions embedded into a Kalman filter. Due to their localizing feature, B‐splines form a highly sparse structure in the filter measurement model. Thus, matrix operations for large‐scale problems can be performed fast using sparse matrix operations, as is done in this study. The differential slant total electron content (dSTEC) analysis and the comparison with Jason‐3 altimetry VTEC were performed for validation within selected periods in 2019. The dSTEC analysis shows that the quality of the generated real‐time VTEC maps slightly outperforms those provided by the other IGS analysis centers.

Description: Plain Language Summary: As part of the Earth's upper atmosphere, the ionosphere is coupled to the Sun and the Earth's lower atmosphere by complex electromagnetic and dynamic interactions of charged particles (electrons and ions) and neutral species. Spatio‐temporal variations of the ionosphere electron content are of particular importance for technologies utilizing electromagnetic signals such as navigation and telecommunication since the electromagnetic waves are refracted/reflected while traveling through the ionosphere. There has been an increasing demand for real‐time ionosphere products to compute interactions between electromagnetic waves and the ionosphere in real‐time. In this context, the IGS and its several analysis centers have been developing models to provide global Vertical Electron Content (VTEC) products using different approaches based on Global Navigation Satellite Systems (GNSS) observations. By considering the crucial impact of the ionosphere and its constituents on our life, in this study, we model the ionosphere VTEC represented by B‐splines embedded into a Kalman filter in real‐time using carrier‐phase observations from geodetic GNSS receivers.

Description: Key Points: A new real‐time approach estimating simultaneously coefficients of the B‐spline representation and biases of carrier‐phases was introduced. Carrier‐phase observations from GPS, GLONASS, and GALILEO were incorporated into an adaptive Kalman filter. Global Navigation Satellite Systems (GNSS) observations were obtained in Radio Technical Commission for Maritime Services format via the International GNSS Service real‐time service.

Description: Technical University of Munich http://dx.doi.org/10.13039/501100005713

Description: German Research Foundation

Description: Bundeswehr GeoInformation Center

Description: German Space Situational Awareness Centre

Description: 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.

Description: The Kalman filter (KF) is widely applied in (ultra) rapid and (near) real-time ionosphere modeling to meet the demand on ionosphere products required in many applications extending from navigation and positioning to monitoring space weather events and naturals disasters. The requirement of a prior definition of the stochastic models attached to the measurements and the dynamic models of the KF is a drawback associated with its standard implementation since model uncertainties can exhibit temporal variations or the time span of a given test data set would not be large enough. Adaptive methods can mitigate these problems by tuning the stochastic model parameters during the filter run-time. Accordingly, one of the primary objectives of our study is to apply an adaptive KF based on variance component estimation to compute the global Vertical Total Electron Content (VTEC) of the ionosphere by assimilating different ionospheric GNSS measurements. Secondly, the derived VTEC representation is based on a series expansion in terms of compactly supported B-spline functions. We highlight the morphological similarity of the spatial distributions and the magnitudes between VTEC values and the corresponding estimated B-spline coefficients. This similarity allows for deducing physical interpretations from the coefficients. In this context, an empirical adaptive model to account for the dynamic model uncertainties, representing the temporal variations of VTEC errors, is developed in this work according to the structure of B-spline coefficients. For the validation, the differential slant total electron content (dSTEC) analysis and a comparison with Jason-2/3 altimetry data are performed. Assessments show that the quality of the VTEC products derived by the presented algorithm is in good agreement, or even more accurate, with the products provided by IGS ionosphere analysis centers within the selected periods in 2015 and 2017. Furthermore, we show that the presented approach can be applied to different ionosphere conditions ranging from very high to low solar activity without concerning time-variable model uncertainties, including measurement error and process noise of the KF because the associated covariance matrices are computed in a self-adaptive manner during run-time.

Description: For more than two decades the IGS (International GNSS Service) Ionosphere Associated Analysis Centers (IAAC) provide global maps of the vertical total electron content (VTEC). In general, the representation of a two- or three-dimensional function can be performed by means of a series expansion or by using a discretization technique. Whereas in the latter case for a spherical function such as VTEC usually pixels or voxels are chosen, in case of a series expansion mostly spherical harmonics (SH) are used as basis functions. The selection of the best suited approach for ionosphere modelling means a trade-off between the distribution of available data and their possibility to represent ionospheric variations with high resolution and high accuracy. Most of the IAACs generate Global Ionosphere Maps (GIMs) based on SH expansions up to the spectral degree n = 15 and provide them with a spatial resolution of 2.5° × 5° with respect to latitude and longitude direction, and a temporal sampling of two hours. In the recent years it was frequently claimed to improve the spatial sampling of the VTEC GIMs to a spatial resolution of 1° × 1° and to a temporal sampling of about 15 minutes. Enhancing the grid resolution means a interpolation of VTEC values for intermediate points but with no further information about variations in the signal. A degree 15 in the SH case for instance corresponds to a spatial sampling of 12° × 12°. Consequently, increasing the grid resolution requires at the same time an extension of the spectral content, i.e. to choose a higher SH degree value than 15. Unlike most of the IAACs, the VTEC modelling approach at DGFI-TUM is based on localizing basis functions, namely tensor products of polynomial and trigonometric B-splines. This way, not only data gaps can be handled appropriately and sparse normal equation systems are established for the parameters estimation procedure, also a multi-scale-representation (MSR) can be set up, to determine GIMs of different spectral content directly by applying the so-called pyramid algorithm and to perform highly effective data compression techniques. The estimation of the MSR model parameters is finally performed by a Kalman-Filter driven by near real-time (NRT) GNSS data. Within this paper we realize the MSR and create multi-scale products based on B-spline scaling and wavelet coefficients and VTEC grid values. We compare these products with different final and rapid products of the IAACs, e.g., the SH model from CODE (Berne) and the voxel solution from UPC (Barcelona). In opposite to that, DGFI-TUM's products are solely based on NRT GNSS observations and ultra-rapid orbits. Nevertheless, we can conclude that DGFI-TUMs high-resolution product (`othg') outperforms all products used within the selected time span of investigation, namely September 2017.

Description: For more than 2 decades the IGS (International GNSS Service) ionosphere associated analysis centers (IAACs) have provided global maps of the vertical total electron content (VTEC). In general, the representation of a 2-D or 3-D function can be performed by means of a series expansion or by using a discretization technique. While in the latter case, pixels or voxels are usually chosen for a spherical function such as VTEC, for a series expansion spherical harmonics (SH) are primarily used as basis functions. The selection of the best suited approach for ionosphere modeling means a trade-off between the distribution of available data and their possibility of representing ionospheric variations with high resolution and high accuracy. Most of the IAACs generate global ionosphere maps (GIMs) based on SH expansions up to the spectral degree n=15 and provide them with a spatial resolution of 2.5∘×5∘ with respect to the latitudinal and longitudinal directions, respectively, and a temporal sampling interval of 2 h. In recent years, it has frequently been claimed that the spatial resolution of the VTEC GIMs has to be increased to a spatial resolution of 1∘×1∘ and to a temporal sampling interval of about 15 min. Enhancing the grid resolution means an interpolation of VTEC values for intermediate points but with no further information about variations in the signal. n=15 in the SH case, for instance, corresponds to a spatial sampling of 12∘×12∘. Consequently, increasing the grid resolution concurrently requires an extension of the spectral content, i.e., to choose a higher SH degree value than 15. Unlike most of the IAACs, the VTEC modeling approach at Deutsches Geodätisches Forschungsinstitut der Technischen Universität München (DGFI-TUM) is based on localizing basis functions, namely tensor products of polynomial and trigonometric B-splines. In this way, not only can data gaps be handled appropriately and sparse normal equation systems be established for the parameter estimation procedure, a multi-scale representation (MSR) can also be set up to determine GIMs of different spectral content directly, by applying the so-called pyramid algorithm, and to perform highly effective data compression techniques. The estimation of the MSR model parameters is finally performed by a Kalman filter driven by near real-time (NRT) GNSS data. Within this paper, we realize the MSR and create multi-scale products based on B-spline scaling, wavelet coefficients and VTEC grid values. We compare these products with different final and rapid products from the IAACs, e.g., the SH model from CODE (Berne) and the voxel solution from UPC (Barcelona). In contrast to the abovementioned products, DGFI-TUM's products are based solely on NRT GNSS observations and ultra-rapid orbits. Nevertheless, we can conclude that the DGFI-TUM's high-resolution product (“othg”) outperforms all products used within the selected time span of investigation, namely September 2017.

Description: The ionosphere is one of the main error sources in positioning and navigation; thus, information about the ionosphere is mandatory for precise modern Global Navigation Satellite System (GNSS) applications. The International GNSS Service (IGS) and its Ionosphere Associated Analysis Centers (IAAC) routinely provide ionospheric information in terms of global ionosphere maps (final GIM). Typically, these products are modeled using series expansion in terms of spherical harmonics (SHs) with a maximum degree of n=15 and are based on post processed observations from Global Navigation Satellite Systems (GNSS), as well as final satellite orbits. However, precise applications such as autonomous driving or precision agriculture require real-time (RT) information about the ionospheric electron content with high spectral and spatial resolution. Ionospheric RT-GIMs are disseminated via Ntrip protocol using the SSR VTEC message of the RTCM. This message can be streamed in RT, but it is limited for the dissemination of coefficients of SHs of lower degrees only. It allows the dissemination of SH coefficients up to a degree of n=16. This suits to most the SH models of the IAACs, but higher spectral degrees or models in terms of B-spline basis functions, voxels, splines and many more cannot be considered. In addition to the SHs, several alternative approaches, e.g., B-splines or Voxels, have proven to be appropriate basis functions for modeling the ionosphere with an enhanced resolution. Providing them using the SSR VTEC message requires a transfer to SHs. In this context, the following questions are discussed based on data of a B-spline model with high spectral resolution; (1) How can the B-spline model be transformed to SHs in order to fit to the RTCM requirements and (2) what is the loss of detail when the B-spline model is converted to SHs of degree of n=16? Furthermore, we discuss (3) what is the maximum necessary SH degree n to convert the given B-spline model and (4) how can the transformation be performed to make it applicable for real-time applications? For a final assessment, we perform both, the dSTEC analysis and a single-frequency positioning in kinematic mode, using the transformed GIMs for correcting the ionospheric delay. The assessment shows that the converted GIMs with degrees n≥30 coincide with the original B-spline model and improve the positioning accuracy significantly.