Tomographic reconstruction of the ionospheric electron density as a function of space and time

Electron density distribution is the major determining parameter of the ionosphere. Computerized Ionospheric Tomography (CIT) is a method to reconstruct ionospheric electron density image by computing Total Electron Content (TEC) values from the recorded Global Positioning Satellite System (GPS) signals. Due to the multi-scale variability of the ionosphere and inherent biases and errors in the computation of TEC, CIT constitutes an underdetermined ill-posed inverse problem. In this study, a novel Singular Value Decomposition (SVD) based CIT reconstruction technique is proposed for the imaging of electron density in both space (latitude, longitude, altitude) and time. The underlying model is obtained from International Reference Ionosphere (IRI) and the necessary measurements are obtained from earth based and satellite based GPS recordings. Based on the IRI-2007 model, a basis is formed by SVD for the required location and the time of interest. Selecting the first few basis vectors corresponding to the most significant singular values, the 3-D CIT is formulated as a weighted least squares estimation problem of the basis coefficients. By providing significant regularization to the tomographic inversion problem with limited projections, the proposed technique provides robust and reliable 3-D reconstructions of ionospheric electron density.     

The use of ionospheric tomography and elevation masks to reduce the overall error in single-frequency GPS timing applications

Signals from Global Positioning System (GPS) satellites at the horizon or at low elevations are often excluded from a GPS solution because they experience considerable ionospheric delays and multipath effects. Their exclusion can degrade the overall satellite geometry for the calculations, resulting in greater errors; an effect known as the Dilution of Precision (DOP). In contrast, signals from high elevation satellites experience less ionospheric delays and multipath effects. The aim is to find a balance in the choice of elevation mask, to reduce the propagation delays and multipath whilst maintaining good satellite geometry, and to use tomography to correct for the ionosphere and thus improve single-frequency GPS timing accuracy. GPS data, collected from a global network of dual-frequency GPS receivers, have been used to produce four GPS timing solutions, each with a different ionospheric compensation technique. One solution uses a 4D tomographic algorithm, Multi-Instrument Data Analysis System (MIDAS), to compensate for the ionospheric delay. Maps of ionospheric electron density are produced and used to correct the single-frequency pseudorange observations. This method is compared to a dual-frequency solution and two other single-frequency solutions: one does not include any ionospheric compensation and the other uses the broadcast Klobuchar model. Data from the solar maximum year 2002 and October 2003 have been investigated to display results when the ionospheric delays are large and variable. The study focuses on Europe and results are produced for the chosen test site, VILL (Villafranca, Spain). The effects of excluding all of the GPS satellites below various elevation masks, ranging from 5° to 40°, on timing solutions for fixed (static) and mobile (moving) situations are presented. The greatest timing accuracies when using the fixed GPS receiver technique are obtained by using a 40° mask, rather than a 5° mask. The mobile GPS timing solutions are most accurate when satellites at lower elevations continue to be included: using a mask between 10° and 20°. MIDAS offers the most accurate and least variable single-frequency timing solution and accuracies to within 10 ns are achieved for fixed GPS receiver situations. Future improvements are anticipated by combining both GPS and Galileo data towards computing a timing solution.     

Computerized ionospheric tomography with the IRI model

Computerized ionospheric tomography (CIT) is a method to estimate ionospheric electron density distribution by using the global positioning system (GPS) signals recorded by the GPS receivers. Ionospheric electron density is a function of latitude, longitude, height and time. A general approach in CIT is to represent the ionosphere as a linear combination of basis functions. In this study, the model of the ionosphere is obtained from the IRI in latitude and height only. The goal is to determine the best representing basis function from the set of Squeezed Legendre polynomials, truncated Legendre polynomials, Haar Wavelets and singular value decomposition (SVD). The reconstruction algorithms used in this study can be listed as total least squares (TLS), regularized least squares, algebraic reconstruction technique (ART) and a hybrid algorithm where the reconstruction from the TLS algorithm is used as the initial estimate for the ART. The error performance of the reconstruction algorithms are compared with respect to the electron density generated by the IRI-2001 model. In the investigated scenario, the measurements are obtained from the IRI-2001 as the line integral of the electron density profiles, imitating the total electron content estimated from GPS measurements. It has been observed that the minimum error between the reconstructed and model ionospheres depends on both the reconstruction algorithm and the basis functions where the best results have been obtained for the basis functions from the model itself through SVD.     

Demonstration of the use of the Doppler Orbitography and Radio positioning Integrated by Satellite (DORIS) measurements to validate GPS ionospheric imaging

There is a lack of independent ionospheric data that can be used to validate GPS imaging results at mid latitudes over severe storm times. Doppler Orbitography and Radio positioning Integrated by Satellite (DORIS), a global network of dual-frequency ground to satellite observations, provides this missing data and here is employed as verification to show the accuracy of the ionospheric GPS images in terms of the total electron content (TEC). In this paper, the large-scale ionospheric structures that appeared during the strong geomagnetic storm of 20 November 2003 are reconstructed with a GPS tomographic algorithm, known as MIDAS, and validated with DORIS TEC measurements. The main trough shown in an extreme equatorward position in the ionospheric imaging over mainland Europe is confirmed by DORIS satellite measurements. Throughout the disturbed day, the variations of relative slant TECs between DORIS data and MIDAS results agree quite well, with the average of the mean differences about 2 TECu. We conclude that as a valuable supplement to GPS data, DORIS ionospheric measurements can be used to analyse TEC variations with a relatively high resolution, ∼10 s in time and tens of kilometres in space. This will be very helpful for identification of some highly dynamic structures in the ionosphere found at mid-latitudes, such as the main trough, TID (Travelling Ionospheric Disturbances) and SED (Storm Enhanced Density), and could be used as a valuable auxiliary data source in ionospheric imaging.     

GPS scintillation and TEC gradients at equatorial latitudes in April 2006

We use observations of ionospheric scintillation at equatorial latitudes from two GPS receivers specially modified for recording, at a sampling rate of 50 Hz, the phase and the amplitude of the L1 signal and the Total Electron Content (TEC) from L1 and L2. The receivers, called GISTM (GPS Ionospheric Scintillation and TEC Monitor), are located in Vietnam (Hue, 16.4°N, 107.6°E; Hoc Mon, 10.9°N, 106.6°E). These experimental observations are analysed together with the tomographic reconstruction of the ionosphere produced by the Multi-Instrument Data Analysis System (MIDAS) for investigating the moderate geomagnetic storm which occurred on early April 2006, under low solar activity. The synergic adoption of the ionospheric imaging and of the GISTM measurements supports the identification of the scale-sizes of the ionospheric irregularities causing scintillations and helps the interpretation of the physical mechanisms generating or inhibiting the appearance of the equatorial F layer irregularities. In particular, our study attributes to the turning of the IMF (Interplanetary Magnetic Field) between northward and southward direction an important role in the inhibition of the generation of spread F irregularities resulting in a lack of scintillation enhancement in the post-sunset hours.     

2000年7月和2003年10月大磁暴期间东亚地区中低纬电离层的GPS TEC的响应研究

利用武汉电离层观象台研制的GPS TEC的现报方法及现报系统,对东亚地区GPS台网的观测数据进行处理分析,特别对2000年7月14-18日和2003年10月28日至11月1日两次特大磁暴期间的数据进行了对比考察,文中分析了两次磁暴间的电离层响应,得到对应不同磁暴时段电离层TEC的不同变化情况,着重揭示了TEC赤道异常峰的压缩和移动以及赤道异常随时间的压缩—反弹—恢复的过程,并结合高纬电离层的部分响应机制进行了说明,结果显示,两次磁暴期的电离层响应表现出了各自不同的特点,从而反映出因季节变化引起的高纬电离层暴时能量注入的不同而造成的全球性电离层扰动的不同形态,由此看出,磁暴期间电离层TEC的变化直接与太阳扰动发生的时间及其对高纬电离层的耦合有关,若短时期内连续发生多次磁暴,则电离层反应更加复杂,不能简单地当做单一磁暴叠加处理。     

A new inversion algorithm for HF sky-wave backscatter ionograms

HF sky-wave backscatter sounding system is capable of measuring the large-scale, two-dimensional (2-D) distributions of ionospheric electron density. The leading edge (LE) of a backscatter ionogram (BSI) is widely used for ionospheric inversion since it is hardly affected by any factors other than ionospheric electron density. Traditional BSI inversion methods have failed to distinguish LEs associated with different ionospheric layers, and simply utilize the minimum group path of each operating frequency, which generally corresponds to the LE associated with the F₂ layer. Consequently, while the inversion results can provide accurate profiles of the F region below the F₂ peak, the diagnostics may not be so effective for other ionospheric layers. In order to resolve this issue, we present a new BSI inversion method using LEs associated with different layers, which can further improve the accuracy of electron density distribution, especially the profile of the ionospheric layers below the F₂ region. The efficiency of the algorithm is evaluated by computing the mean and the standard deviation of the differences between inverted parameter values and true values obtained from both vertical and oblique incidence sounding. Test results clearly manifest that the method we have developed outputs more accurate electron density profiles due to improvements to acquire the profiles of the layers below the F₂ region. Our study can further improve the current BSI inversion methods on the reconstruction of 2-D electron density distribution in a vertical plane aligned with the direction of sounding.     

地磁暴期间中国中低纬电离层的CIT研究

利用电离层层析成像技术(Computerized Ionospheric Tomography, CIT)处理115°E子午圈附近6个台站的GPS观测数据, 分析了2004年11月地磁暴期间中国中低纬电离层的响应情况. 结果表明, 电离层呈正相扰动, 且不同高度上的响应不同, 800 km以下电子密度有不同程度的增加, 且在峰值高度附近增幅最大, 800 km以上地磁暴的影响并不显著; 伴随地磁能量的注入, 赤道异常峰极向扩展; 随磁扰强度的降低, 电子密度也逐渐恢复至平静水平. 这些结果与以往的理论和观测结果一致, 初步估计扰动是由热层暴环流引起的, 并受到赤道异常峰移动的影响.      

Regional 4-D modeling of the ionospheric electron density from satellite data and IRI

Accurate knowledge of the electron density is the key point in correcting ionospheric delays of electromagnetic measurements and in studying ionosphere physics. During the last decade Global Navigation Satellite Systems (GNSS) have become a promising tool for monitoring ionospheric parameters such as the total electron content (TEC). In this contribution we present a four-dimensional (4-D) model of the electron density consisting of a given reference part, i.e., the International Reference Ionosphere (IRI), and an unknown correction term expanded in terms of multi-dimensional base functions. The corresponding series coefficients are calculable from the satellite measurements by applying parameter estimation procedures. Since satellite data are usually sampled between GPS satellites and ground stations, finer structures of the electron density are modelable just in regions with a sufficient number of ground stations. The proposed method is applied to simulated geometry-free GPS phase measurements. The procedure can be used, for example, to study the equatorial anomaly.     

Wavelet modelling in support of IRI

The slant total electron content (STEC) of the ionosphere is defined as the integral of the electron density along the ray-path of the signal between the transmitter and the receiver. So-called geometry free GPS measurements provide information on the electron density, which is basically a four-dimensional function depending on spatial position and time. Since ground-based measurements are not very sensitive to the vertical structure within the atmosphere, the ionosphere is often represented by a spherical layer, where all electrons are concentrated. Then the STEC is transformed into the vertical total electron content (VTEC), which is a three-dimensional function depending on longitude, latitude and time.In our approach, we decompose an ionospheric function, i.e. the electron density or the VTEC, into a reference part computed from a given model like the International Reference Ionosphere (IRI) and an unknown correction term expanded in a multi-dimensional series in terms of localizing base functions. The corresponding series coefficients are calculable from GPS measurements applying parameter estimation procedures. Since the GPS receivers are located rather unbalanced, finer structures are modelable just in regions with a sufficient number of observation sites. Due to the localizing feature of B-spline functions we apply a tensor product spline expansion to model the correction term regionally. Furthermore, the multi-resolution representation derived from wavelet analysis allows monitoring the ionosphere at different resolutions levels. We demonstrate the advantages of this procedure by representing a simulated VTEC data set over South America.     

The impact of spherical symmetry assumption on radio occultation data inversion in the ionosphere: An assessment study

‘Onion-peeling’ is a very common technique used to invert Radio Occultation (RO) data in the ionosphere. Because of the implicit assumption of spherical symmetry for the electron density (N(e)) distribution in the ionosphere, the standard Onion-peeling algorithm could give erroneous concentration values in the retrieved electron density profile. In particular, this happens when strong horizontal ionospheric electron density gradients are present, like for example in the Equatorial Ionization Anomaly (EIA) region during high solar activity periods. In this work, using simulated RO Total Electron Content (TEC) data computed by means of the NeQuick2 ionospheric electron density model and ideal RO geometries, we tried to formulate and evaluate an asymmetry level index for quasi-horizontal TEC observations. The asymmetry index is based on the electron density variation that a signal may experience along its path (satellite to satellite link) in a RO event and is strictly dependent on the occultation geometry (e.g. azimuth of the occultation plane). A very good correlation has been found between the asymmetry index and errors related to the inversion products, in particular those concerning the peak electron density NmF2 estimate and the Vertical TEC (VTEC) evaluation.     

A real-time ionospheric model based on GNSS Precise Point Positioning

This paper proposes a method of real-time monitoring and modeling the ionospheric Total Electron Content (TEC) by Precise Point Positioning (PPP). Firstly, the ionospheric TEC and receiver’s Differential Code Biases (DCB) are estimated with the undifferenced raw observation in real-time, then the ionospheric TEC model is established based on the Single Layer Model (SLM) assumption and the recovered ionospheric TEC. In this study, phase observations with high precision are directly used instead of phase smoothed code observations. In addition, the DCB estimation is separated from the establishment of the ionospheric model which will limit the impacts of the SLM assumption impacts. The ionospheric model is established at every epoch for real time application. The method is validated with three different GNSS networks on a local, regional, and global basis. The results show that the method is feasible and effective, the real-time ionosphere and DCB results are very consistent with the IGS final products, with a bias of 1–2 TECU and 0.4 ns respectively.     

Ionospheric path delay models for spaceborne GPS receivers flying in formation with large baselines

GPS relative navigation filters could benefit notably from an accurate modeling of the ionospheric delays, especially over large baselines (>100 km) where double difference delays can be higher than several carrier wavelengths. This paper analyzes the capability of ionospheric path delay models proposed for spaceborne GPS receivers in predicting both zero-difference and double difference ionospheric delays. We specifically refer to relatively simple ionospheric models, which are suitable for real-time filtering schemes. Specifically, two ionospheric delay models are evaluated, one assuming an isotropic electron density and the other considering the effect on the electron density of the Sun aspect angle. The prediction capability of these models is investigated by comparing predicted ionospheric delays with measured ones on real flight data from the Gravity Recovery and Climate Experiment mission, in which two satellites fly separated of more than 200 km. Results demonstrate that both models exhibit a correlation in the excess of 80% between predicted and measured double-difference ionospheric delays. Despite its higher simplicity, the isotropic model performs better than the model including the Sun effect, being able to predict double differenced delays with accuracy smaller than the carrier wavelength in most cases. The model is thus fit for supporting integer ambiguity fixing in real-time filters for relative navigation over large baselines. Concerning zero-difference ionospheric delays, results demonstrate that delays predicted by the isotropic model are highly correlated (around 90%) with those estimated using GPS measurements. However, the difference between predicted and measured delays has a root mean square error in the excess of 30 cm. Thus, the zero-difference ionospheric delays model is not likely to be an alternative to methods exploiting carrier-phase observables for cancelling out the ionosphere contribution in single-frequency absolute navigation filters.     

Electron density retrieval from occulting GNSS signals using a gradient-aided inversion technique

In the coming years, opportunities for remote sensing of electron density in the Earth’s ionosphere will expand with the advent of Galileo, which will become part of the global navigation satellite system (GNSS). Methods for accurate electron density retrieval from radio occultation data continue to improve. We describe a new method of electron density retrieval using total electron content measurements obtained in low Earth orbit. This method can be applied to data from dual-frequency receivers tracking the GPS or Galileo transmitters. This simulation study demonstrates that the method significantly improves retrieval accuracy compared to the standard Abel inversion approach that assumes a spherically symmetric ionosphere. Our method incorporates horizontal gradient information available from global maps of Total Electron Content (TEC), which are available from the International GNSS Service (IGS) on a routine basis. The combination of ground and space measurements allows us to improve the accuracy of electron density profiles near the occultation tangent point in the E and F regions of the ionosphere.     

基于小波分解与重构方法研究电离层偶发E层

电离层不规则体对卫星导航、通信、雷达系统等有重要影响.通过数值模拟及与实测数据的对比,论证基于小波分解与重构方法实现利用掩星数据反演电离层不规则体的可行性.以电离层偶发E层为例,利用国际参考电离层(IRI)模拟背景电离层电子密度分布,利用掩星探测的水平电子密度总含量δht反演不规则体信息,并与模拟数据进行比较.对200...     

Evaluation of the IRI-2016 and NeQuick electron content specification by COSMIC GPS radio occultation,ground-based GPS and Jason-2 joint altimeter/GPS observations

We examined performance of two empirical profile-based ionospheric models, namely IRI-2016 and NeQuick-2, in electron content (EC) and total electron content (TEC) representation for different seasons and levels of solar activity. We derived and analyzed EC estimates in several representative altitudinal intervals for the ionosphere and the plasmasphere from the COSMIC GPS radio occultation, ground-based GPS and Jason-2 joint altimeter/GPS observations. It allows us to estimate a quantitative impact of the ionospheric electron density profiles formulation in several altitudinal intervals and to examine the source of the model-data discrepancies of the EC specification from the bottom-side ionosphere towards the GPS orbit altitudes. The most pronounced model-data differences were found at the low latitude region as related to the equatorial ionization anomaly appearance. Both the IRI-2016 and NeQuick-2 models tend to overestimate the daytime ionospheric EC and TEC at low latitudes during all seasons of low solar activity. On the contrary, during high solar activity the model results underestimated the EC/TEC observations at low latitudes. We found that both models underestimated the EC for the topside ionosphere and plasmasphere regions for all levels of solar activity. For low solar activity, the underestimated EC from the topside ionosphere and plasmasphere can compensate the overestimation of the ionospheric EC and, consequently, can slightly decrease the resulted model overestimation of the ground-based TEC. For high solar activity, the underestimated EC from the topside ionosphere and plasmasphere leads to a strengthening of the model underestimation of the ground-based TEC values. We demonstrated that the major source of the model-data discrepancies in the EC/TEC domain comes from the topside ionosphere/plasmasphere system.     

基于BP神经网络技术的电离层VTEC融合

随着电离层探测技术的不断发展，电离层观测资料也越来越多，只使用单一的观测资料会出现电离层反演精度不高的问题。为了提高电离层的反演精度，使用BP神经网络技术将地基反演和国际参考电离层(international reference ionosphere，IRI)模型的垂直总电子含量（vertical total electron content，VTEC）数据进行有效融合。在温带地区\[35°(N)~45°(N)，60°(E)~80°(E)\]进行电离层反演试验，结果表明基于BP神经网络技术的电离层数据融合和地基反演获得的电离层VTEC精度都比较高，但是基于BP神经网络的电离层数据融合反演精度比地基反演更高，所以基于BP神经网络技术的数据融合能够提高电离层的反演精度。     

Variations of quasi-electrostatic fields and ionosphere potential above lightning discharge at equatorial latitudes

Lightning discharges by thunderstorms cause generation of electromagnetic pulses and of quasi-electrostatic fields (QESF) in the atmosphere above, which occur in different time-scales. QESF penetrate into the mesosphere and the lower ionosphere where they are big enough to generate considerable electric charge transfer there and, in some cases, to cause red sprites. These processes may have an important contribution to the global atmospheric electric circuit. Significant transient variations of the ionospheric potential above the thunderstorm take place as well. QESF depend on the atmospheric conductivity and in the ionosphere they are affected also by its anisotropy determined by geomagnetic field orientation. QESF after a lightning discharge are investigated theoretically in this work in the case of equatorial latitudes (by horizontal geomagnetic field), where thunderstorms are important contributors to the global circuit. Results for DC electric fields in the lower equatorial ionosphere above a thundercloud obtained by earlier models demonstrate some specific features of the spatial distribution of these fields, which appear due to geomagnetic field orientation. Thus, the electric fields can be shifted by tens or more kilometers to east of the cloud charge region; also their horizontal scale is much bigger than in the case of middle latitudes. Here, a presence of similar specific features of quasi-electrostatic field distributions and ionospheric potential variations caused by a lightning stroke is studied. A situation when no secondary ionization is generated is considered. A model based on the Maxwell equations for potential electric fields is proposed. Computations of QESF in the middle atmosphere and of the ionospheric potential variations are provided as dependent on conductivity and its anisotropy in D-region. The obtained results for the ionosphere show that the electric fields in the equatorial lower ionosphere are comparable to these formed in the case of middle latitudes. However, their horizontal scales are much bigger and depend on conductivity profiles. Similar features are valid also for the ionospheric potential variations and for their horizontal scales.     

Model based Computerized Ionospheric Tomography in space and time

Reconstruction of the ionospheric electron density distribution in space and time not only provide basis for better understanding the physical nature of the ionosphere, but also provide improvements in various applications including HF communication. Recently developed IONOLAB-CIT technique provides physically admissible 3D model of the ionosphere by using both Slant Total Electron Content (STEC) measurements obtained from a GPS satellite - receiver network and IRI-Plas model. IONOLAB-CIT technique optimizes IRI-Plas model parameters in the region of interest such that the synthetic STEC computations obtained from the IRI-Plas model are in accordance with the actual STEC measurements. In this work, the IONOLAB-CIT technique is extended to provide reconstructions both in space and time. This extension exploits the temporal continuity of the ionosphere to provide more reliable reconstructions with a reduced computational load. The proposed 4D-IONOLAB-CIT technique is validated on real measurement data obtained from TNPGN-Active GPS receiver network in Turkey.     

Low-latitude ionospheric scintillations and total electron content obtained with the CITRIS instrument on STPSat1 using radio transmissions from DORIS ground beacons

The primary objective of the Scintillation and Tomography Receiver in Space (CITRIS) is to detect ionospheric irregularities from space at low latitude. For this purpose, the satellite receiver uses the UHF and S-Band transmissions of the ground network of Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS) beacons. CITRIS, developed at the Naval Research Laboratory, differs from the normal DORIS receiver by being able to capture and store the complex amplitude of the 401.25 and 2036.25 MHz transmissions at 200 Hz sample rate. Ground processing of the CITRIS data yields total electron content (TEC) and both phase and amplitude scintillations. With CITRIS flying on the US Space Test Program (STP) satellite STPSat1, 2 years of data were collected and processed to determine the fluctuations in ionospheric TEC and radio scintillations associated with equatorial irregularities. CITRIS flights over DORIS transmitters yield direct measurements of the horizontal plasma density fluctuations associated with equatorial plasma bubbles. Future flights of CITRIS can provide valuable complements to other satellite instruments such as GPS occultation receivers used to estimate vertical electron density profiles in the ionosphere.