Three-dimensional ionospheric tomography by an improved algebraic reconstruction technique

Ionospheric tomography is a technique whereby a vertical cross section through ionospheric electron density can be imaged. The vertical resolution of ionospheric tomography systems is inherently poor, but can be improved by using a priori information in the tomographic reconstruction algorithm. Care must be exercised in using a priori information, since if too much of it is used, the reconstruction algorithm may discard some of the information contained in the tomographic data in favor of satisfying some of the a priori assumptions. Orthogonal decomposition (OD) is an existing technique that uses a priori information to constrain the reconstruction to lie in a space of reasonable images without weighting the reconstruction toward any particular a priori image. In this way a priori information can be used in a manner that does not overwhelm information contained in the data. Gauss-Seidel (GS) is an iterative algorithm that is used to calculate solutions for large systems of linear equations. In this article, a block version of the GS algorithm will be used to calculate the solution of the least-squares problem that is created using OD. The complete algorithm presented here will be called the residual correction method (RCM), since it involves calculation of successively better approximations based on the residual error. RCM is a fast and numerically stable algorithm that extracts as much information from the data as possible. A numerical example demonstrating the properties of RCM will also be presented. © 1996 John Wiley & Sons, Inc.

Data collection for the first ground‐based ionospheric tomography campaign in North America was conducted over a 48‐hour period in mid‐November 1991. The data consist of records of ionospheric total electron content (TEC) from a number of passes of the U. S. Navy Navigation Satellite System spacecraft over a chain of ground‐based receiving stations. Data collection and reduction techniques are discussed; these include the determination of absolute TEC from the different phase advances induced by the ionosphere in each component of the dual‐frequency spacecraft signal. The use of tomographic methods to reconstruct ionospheric electron densities over a two‐dimensional (2‐D) region of the Earth's ionosphere at a number of different times is demonstrated. Specifically, two distinct tomographic methods, the algebraic reconstruction technique and a maximum entropy method, are used to mathematically invert the records of TEC. The resulting 2‐D contour “maps” of ionospheric electron density are then compared to similar maps produced by the Millstone Hill incoherent backscatter radar facility located at Westford, Massachusetts. Both qualitative and quantitative measures of agreement among the different reconstructions and the radar maps are presented. The behavior of the ionosphere over the course of the experiment is discussed.

To generate high-quality reconstructions of ionospheric electron density (IED), we propose an extended simultaneous algebraic reconstruction technique (ESART). The ESART method distributes the discrepancy between the actual GNSS TEC and the calculated TEC among the ray–voxels based on the contribution of voxels to GNSS TEC, rather than the ratio of the length of ray–voxel intersection to the sum of the lengths of all ray–voxel intersections, as is adopted by conventional methods. The feasibility of the ESART method for reconstructing the IED under different levels of geomagnetic activities is addressed. Additionally, a preliminary experiment is performed using the reconstructed IED profiles and comparing them with ionosonde measurements, which provide direct observations of electron density. The root mean square errors (RMSE) and absolute errors of the ESART method, the simultaneous algebraic reconstruction technique (SART) method, and the International Reference Ionosphere (IRI) 2016 model are calculated to evaluate the effectiveness of the proposed method. Compared to the conventional SART method of ionospheric tomography and the IRI-2016 model, the reconstructed IED profiles obtained using the ESART method are in better agreement with the electron density obtained from the ionosondes, especially for the peak electron densities (NmF2). In addition, a case study of an intense geomagnetic storm on 17–19 March 2015 shows that the spatial and temporal features of storm-related ionospheric disturbances can be more clearly depicted using the ESART method than with the SART method.

High-accuracy Total Electron Content (TEC) measurements are important for several applications, including GNSS time transfer with accuracies better than 10 ns. In addition, it is important to provide uncertainty estimates to algorithms that use the TEC measurements. Dual-frequency TEC errors are dominated by satellite inter-frequency biases, satellite inter-code biases, receiver inter-frequency biases, receiver noise and multipath, higher-order ionospheric errors, and receiver inter-code biases for certain receivers. To evaluate different algorithms and error mitigation methods, data were collected from four different GPS receivers in two locations at the Arecibo Observatory in Puerto Rico. Error mitigation methods include receiver hardware bias calibration, comparison with TEC maps provided by the Jet Propulsion Laboratory (JPL), receiver comparisons, TEC calibration during low TEC count as determined by the Arecibo radar, and multipath mitigation using the Code Noise Multi-Path (CNMP) algorithm [12]. The CNMP algorithm enables the definition of rigorous multipath error bounds on the TEC bias estimation.

This paper focuses on the linkage between reverse fountain effect and anomalous enhancement in the nighttime electron density over the equatorial ionosphere often referred as the ionospheric nighttime enhancement (INE). The Global Positioning System (GPS)‐derived total electron content (TEC) measurements over two Indian equatorial stations and ionosonde measurements are used to investigate the occurrence characteristics and mechanism of the premidnight and postmidnight INE events. The high‐resolution spatiotemporal two‐dimensional (2D) TEC maps generated by using satellite‐based augmentation system are used to visualize the reverse fountain effect. These TEC maps are found to be effective in envisaging the motion of equatorial ionization anomaly (EIA) in nighttime ionosphere and its impact on the distribution of electron density over the equatorial region. Salient features of this case study illustrate that, accompanying enhancements in the nighttime TEC, there exist decrease in the F2 layer height, prevalence of downward vertical plasma drift, and dramatic increase in the F2 region electron density. The 2D‐TEC maps reveal the persistence of well‐developed EIA until late evening hours and its gradual shift toward equator during the events of postmidnight INEs. It is found out that the premidnight INE is not invariably linked to the prereversal enhancement of the zonal electric field and could be associated with the redistribution of electron density caused by the reverse fountain effect. The present observations indicate that although the westward electric field serves as a prime driver, the INEs over the equatorial regions are associated with plasma motions caused by the retreating anomaly.

Application of hybrid regularization method for tomographic reconstruction of midlatitude ionospheric electron density

Ionospheric total electron content (TEC) measurements, obtained simultaneously at several locations, can be processed using computerized tomography (CT) algorithms to obtain two‐dimensional images of ionospheric electron density. Using TEC data, computerized ionospheric tomography (CIT) reconstructs an image of the electron density structures in a vertical slice above the receiving stations. We successfully applied this technique to realistic simulations of ionospheric density variations over 16° of latitude and a height range of 50 to 1000 km. A method for approximating the peak height and scale height of the electron density profile will be discussed as well as a reconstruction technique based on the multiplicative algebraic reconstruction technique algorithm and a back projection based initial guess. The quality of reconstructions is considered for two geometries and image resolutions. In particular, the image of a mid‐latitude trough with background horizontal density gradient and large‐scale irregular structures has been reconstructed from TEC data generated from a model based on an incoherent scatter radar observation. The CT reconstructed image was compared with the original contour map obtained by the incoherent scatter radar. Good agreement has been achieved. The CIT technique has also been applied to a modeled ionosphere to calculate the range rate corrections for a Doppler‐tracking radar.

The blockage of solar radiation causes a sudden decrease in electron density in the shadow region of Earth’s ionosphere during the total solar eclipse period. After the eclipse, the ionospheric electron density returns to its normal daytime conditions. Thus, the solar eclipse is a wonderful opportunity to study the ionospheric electron density variation in the absence of solar radiation for a short duration. To better correlate the effects of the eclipse on ionospheric electron density distribution, the eclipse obscuration percentage along each satellite IPP trajectories is derived. Compared to non-eclipse days, clear depletions in the TEC values are observed in all the stations after the eclipse onset. The time lags are attributed to the lifetime of charged particles at various ionospheric layers.

Application of ionospheric tomography inversion to GPS data to study ionospheric electron-density distribution over China

For the first time, post-midnight Equatorial Plasma Depletions (EPDs) have been imaged in the longitude-altitude plane using radio-beacon tomography. High-resolution (~10 km × 10 km) electron-density reconstructions were created in the area between approximately -90° and -55° longitude near the geomagnetic equator. The reconstructions were created using Total Electron Content (TEC) measurements from an NRL receiver array sited in Peru and the MART inversion algorithm. TEC was derived from the 150 and 400 MHz signals transmitted by the CERTO beacon on the C/NOFS satellite. The MART algorithm requires an “initial guess” ionosphere, which was generated by using in-situ electron density data from the C/NOFS CINDI instrument and electron density profiles from an ionosonde operated by the University of Massachusetts at Lowell (UML). Each initial guess ionosphere was approximated below the F-peak by replicating an ionosonde profile over all longitudes within the imaging region; above the F-peak a Chapman function was fitted to the ionosonde F-peak density and the corresponding CINDI in-situ measurement at each longitude. In this study, EPDs spawned pre-midnight were imaged near dawn. Observed EPDs had widths of 100-1000 km, spacings of 300-900 km, and often appeared “pinched off” at the bottom. Well-developed EPDs appeared on an evening with a very small (4 m/s) Pre-Reversal-Enhancement (PRE), suggesting that postmidnight enhancements of the vertical plasma drift and/or seeding-induced uplifts (e.g. gravity waves) were responsible for driving the Rayleigh-Taylor Instability into the nonlinear regime on this night. On another night the Jicamarca incoherent scatter radar recorded postmidnight (~0230 LT) Eastward electric fields nearly twice as strong as the PRE fields seven hours earlier. These electric fields lifted the whole ionosphere, including embedded EPDs, over a longitude range ~14° wide. CINDI detected a dawn depletion in exactly the area where the reconstruction showed an uplifted EPD. Strong Equatorial Spread-F observed by the UML ionosonde during receiver observation times confirmed the presence of ionospheric irregularities.

In this study, the two-dimensional horizontal structure of EPB was observed using GPS total electron content (TEC) measurement in South East Asia region. Rate of TEC index (ROTI) is calculated from GPS TEC measurement and plotted onto two-dimensional map in geographic coordinate. Depletion of The OI 630.0 nm emission is completely coincided with ROTI enhancement region from GPS TEC measurement. Therefore, the observation using GPS TEC measurement is able to provide spatial and temporal properties of EPB in SEA region.

Global ionospheric mapping (GIM) is a new and emerging technique for determining global ionospheric TEC (total electron content) based on measurements from a worldwide network of Global Positioning System (GPS) receivers. In this study, GIM accuracy in specifying TEC is investigated by comparison with direct ionospheric measurements from the TOPEX altimeter. A climatological model (Bent model) is also used to compare with the TOPEX altimeter data. We find that the GIM technique has much better agreement with TOPEX in TEC measurements, compared with the predictions of the climatological model. The difference between GIM and TOPEX in TEC measurements is very small (less than 1.5 TEC units (TECU)) within a 1500‐km range from a reference GPS station. The RMS gradually increases with increasing distance from the station, while the Bent model shows a constant large RMS, unrelated to any station location. Within a 1000‐km distance of a GPS site (elevation angle > 25°), GIM has a good correlation (R > 0.93) to TOPEX with respect to TEC measurements. The slope of the linear fitting line to the data set from two TOPEX cycles is 44.5° (near the ideal 45°). In the northern hemispheric regions, ionospheric specification by GIM appears to be accurate to within 3‐10 TECU up to 2000+ km away from nearest GPS station (corresponding to ∼1° elevation angle cutoff). Beyond 2000 km, GIM accuracy, on average, is reduced to the Bent model levels. In the equatorial region, the Bent model predictions are systematically lower (∼5.0 TECU) than TOPEX values and often show a saturation at large TEC values. During ionospheric disturbed periods, GIM sometimes shows differences from TOPEX values due to transient variations of the ionosphere. Such problems may be improved by the continuous addition of new GPS stations in data‐sparse regions. Thus, over a GPS station's measurement realm (up to 2000 km in radius), GIM can produce generally accurate TEC values. Through a spatial and temporal extrapolation of GPS‐derived TEC measurements, the GIM technique provides a powerful tool for monitoring global ionospheric features in near real time.

利用武汉电离层观测站1997-2007年电离层TEC资料, 采用连续小波变换和交叉小波以及小波相干方法, 分析了该站电离层TEC的周期变化特征以及与太阳和地磁活动之间的关系. 分析结果表明, 武汉站TEC变化的长期趋势主要随太阳活动的强弱而变化; 在局部时域上分别存在128～256d, 256～512d和512d～1024d的周期尺度, 且与同时期的太阳黑子数和地磁<I>Dst</I>指数的周期特征存在很好的对应关系; 太阳黑子数在512～1024d周期尺度上超前TEC变化约1/6个周期; 在准半年的周期尺度上武汉站TEC与地磁<I>Dst</I>指数几乎呈反相位变化, 但TEC对$Dst$指数的这种响应仅在太阳活动高年存在, 具体机理尚需进一步分析研究.

Mapping of the Ionospheric Total Electron Content over the East African Low–Latitude Region

Indian regional navigation satellite system (IRNSS) is a navigation system developed by the Indian Space Research Organisation (ISRO), India. The IRNSS receiver granted by Space Application Centre (SAC), ISRO, Ahmedabad is installed at SVNIT, Surat, India. A solar flare is a natural event that occurs when an unpredicted flash of distended Sun's illumination is observed near its surface. The ionosphere is greatly ionised by solar radiations. Hence it is a current challenge to investigate effects of ionospheric scintillation on IRNSS signals. This study examines impact of major solar flare events like Class ‘C’ solar flare happened on 22 July 2016 and class ‘M’ solar flare occurred on 23 and 24 July 2016, on IRNSS signals with measurement of total electron content (TEC). Real-time ionospheric scintillation monitoring (RTISM) model based on empirical mode decomposition (EMD) and second-order Daubechies (db2) wavelet is used for comparing measured and denoised TEC. The RTISM model is also used for determining automatic threshold using Neyman–Pearson detector, probability of detection and probability of false alarm. It is proven with analysis that EMD is giving more sharp results as compared to db2 wavelet for determining fluctuations in TEC during the solar flare events.