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.     

A MARS-based method for estimating regional 2-D ionospheric VTEC and receiver differential code bias

The geometry-free linear combination of dual-frequency GNSS reference station ground observations are currently used to build the Vertical Total Electron Content (VTEC) model of the ionosphere. As it is known, besides ionospheric delays, there are differential code bias (DCB) of satellite (SDCB) and receiver (RDCB) in the geometry-free observation equation. The SDCB can be obtained using the International GNSS Service (IGS) analysis centers, but the RDCB for regional and local network receivers are not provided. Therefore, estimating the RDCB and VTEC model accurately and simultaneously is a critical factor investigated by researchers. This study uses Multivariate Adaptive Regression Splines (MARS) to estimate the VTEC approximate model and then substitutes this model in the observation equation to form the normal equation. The least squares method is used to solve the RDCB and VTEC model together. The research findings show that this method has good modeling effectiveness and the estimated RDCB has good reliability. The estimated VTEC model applied to GPS single-frequency precise point positioning has better positioning accuracy in comparison to the IGS global ionosphere map (GIM).     

Eliminating negative VTEC in global ionosphere maps using inequality-constrained least squares

Currently, ground-based Global Navigation Satellite System (GNSS) stations of the International GNSS Service (IGS) are distributed unevenly around the world. Most of them are located on the mainland, while only a small part of them are scattered on some islands in the oceans. As a consequence, many unreasonable zero values (in fact negative values) appear in Vertical Total Electron Content (VTEC) of European Space Agency (ESA) and Center for Orbit Determination in Europe (CODE) IONEX products, especially in 2008 and 2009 when the solar activities were rather quiet. To improve this situation, we directly implement non-negative physical constraints of ionosphere for global ionosphere maps (GIM) with spherical harmonic functions. Mathematically, we propose an inequality-constrained least squares method by imposing non-negative inequality constraints in the areas where negative VTEC values may occur to reconstruct GIM models. We then apply the new method to process the IGS data in 2008. The results have shown that the new algorithm efficiently eliminates the unwanted behavior of negative VTEC values, which could otherwise often be seen in the current CODE and ESA GIM products in both middle and high latitude areas of the Southern Hemisphere (45°S∼90°S) and the Northern Hemisphere (50°N∼90°N). About 64% of GPS receivers’ DCBs have been significantly improved. Finally, we compare the GIM results between with and without the inequality constraints, which has clearly shown that the GIM result with inequality constraints is significantly better than that without the inequality constraints. The inequality-constrained GIM result is also highly consistent with the final IGS products in terms of root mean squared (RMS) and mean VTEC.     

Using GPS-TEC data to calibrate VTEC computed with the IRI model over Nigeria

This paper presents the development of a Total Electron Content (TEC) map for the Nigerian ionosphere. In this work, TEC measurements obtained from the AFRL-SCINDA GPS (Air Force Research Laboratory-Scintillation Network Decision Aid, Global Positioning System) equipment installed at Nsukka (6.87°N, 7.38°E) are used to adapt the International Reference Ionosphere (IRI) model for the Nigerian Ionosphere. The map is being developed as a computer program (implemented in the MATLAB programming language) that shows spatial and temporal representations of TEC for the Nigerian ionosphere. The method is aimed at showing how the IRI model can be used to estimate VTEC over wide areas by incorporating GPS measurements. This method is validated by using GPS VTEC data collected from a station in Ilorin (8.50°N, 4.55°E).     

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。     

Regional VTEC modeling with multivariate adaptive regression splines

Different algorithms have been proposed for the modeling of the ionosphere. The most frequently used method is based on the spherical harmonic functions achieving successful results for global modeling but not for the local and regional applications due to the bounded spherical harmonic representation. Irregular data distribution and data gaps cause also difficulties in the global modeling of the ionosphere. In this paper we propose an efficient algorithm with Multivariate Adaptive Regression Splines (MARS) to represent a new non-parametric approach for regional spatio-temporal mapping of the ionospheric electron density using ground-based GPS observations. MARS can handle very large data sets of observations and is an adaptive and flexible method, which can be applied to both linear and non-linear problems. The basis functions are directly obtained from the observations and have space partitioning property resulting in an adaptive model. This property helps to avoid numerical problems and computational inefficiency caused by the number of coefficients, which has to be increased to detect the local variations of the ionosphere. Since the fitting procedure is additive it does not require gridding and is able to process large amounts of data with large gaps. Additionally the model complexity can be controlled by the user via limiting the maximal number of coefficients and the order of products of the basis functions. In this study the MARS algorithm is applied to real data sets over Europe for regional ionosphere modeling. The results are compared with the results of Bernese GPS Software over the same region.     

Improved predictions of equatorial TEC for real time applications

It is important to use models developed specifically for the equatorial ionospheric estimation for real-time applications, particularly in Satellite Navigation. This work demonstrates a methodology for improved predictions of VTEC in real time using the model developed for the equatorial ionosphere by the authors. This work has been done using TEC data of the low solar activity period of 2005 obtained using dual frequency GPS receivers installed under the GAGAN project of ISRO. For the purpose, the model is first used in conjunction with Kriging technique. Improvement in accuracy is observed when compared with the estimations from the model alone using the measurements as true reference. Further improvement is obtained by Bayesian combination of these estimates with independent Neural Network based predictions. Statistical performance of improvement is provided. An improvement of ∼1 m in confidence level of estimation of VTEC is obtained.     

Analysis of the data processing strategies of spherical harmonic expansion model on global ionosphere mapping for moderate solar activity

Spherical harmonic (SH) expansion is widely used to model the global ionosphere map (GIM) of vertical total electron content (VTEC). According to the impact of different data processing methods of the SH expansion model on the VTEC maps, we specifically performed comprehensive analysis in terms of the data sampling rate, the time resolution, the spherical harmonic degree, and the relative constraint. One month of GPS data (January in 2016) from the International GNSS (Global Navigation Satellite System) Service (IGS) network in a moderate ionospheric activity period at the descending phase of Solar Cycle 24 was processed. To improve the computational efficiency of the daily GIM generation, the data sampling rate of 5?min was recommended allowing the GIM precision loss within 0.10 TECU (total electron content unit). The global VTEC map could be better represented in temporal and spatial domains with higher time resolution and higher spherical harmonic degree, especially at low latitude bands and in the southern hemisphere. The GIM precision improvement was about 10.91% for 1-h and about 15.15% for 0.5-h compared with the commonly used 2-h time resolution. The use of spherical harmonic degree 17 or 20 instead of 15 could improve the precision by 3.19% or 6.06%. We also found that an optimal relative constraint had to be found experimentally considering both the GIM precision and the GIM root mean square (RMS) map.     

Negative VTEC with spherical harmonic expansion model under different solar activity conditions

The Earth’s ionosphere can be described by a spherical harmonic (SH) expansion up to a specific degree. However, there exist negative vertical total electron content (VTEC) values in the global ionosphere map (GIM) with the SH expansion model. In this contribution, we specifically investigated the negative VTEC values that are induced by the SH expansion model and validated the performance of the inequality-constrained least squares (ICLS) method in eliminating the negative VTEC values. The GPS data from 2004 to 2017 was selected to cover one solar cycle and the experiments under different solar activity conditions were analyzed. The results in our work show that the occurrence of the negative VTEC values is attributed to the deficiency of the SH expansion model when the VTEC itself is small instead of the unevenly distribution of the GNSS stations. The negative VTEC values appear periodically in the temporal domain, showing apparently one year and half year periods. During one year, two peaks in June and December can be observed in the time series of the negative VTEC values. The number of negative VTEC values in June is obvious larger than that in December. During one solar cycle, the number of negative VTEC values under quiet solar activity condition is obvious larger than that under strong solar activity condition. In the spatial domain, the appearance of the negative VTEC values is strongly related with the movement of the subsolar point. In the latitude of the subsolar point has the largest magnitude, the negative values will appear on the opposite hemisphere and the further from the subsolar point the more negative values. The maximum number of the negative VTEC values in the southern hemisphere appears in June, while the peak value in the northern hemisphere appears in December. The maximum number of negative VTEC values in the southern hemisphere is generally larger than that in the northern hemisphere. In addition, the negative VTEC values are distributed both at middle latitude and high latitude in the southern hemisphere, while they are mainly distributed at high latitude in the northern hemisphere. When the ICLS method is used, the negative VTEC values can be eliminated efficiently and it has nearly no influence on the positive VTEC values. The ICLS method can also improve the receiver’s differential code bias (DCB) and significantly decrease the unreasonable negative slant TEC (STEC) values along the lines of sight. Using the final GIM product of the Jet Propulsion Laboratory (JPLG) as a reference, the root mean square (RMS) of the ICLS solution shows maximum 25%, 20% and 45% improvement relative to the least squares (LS) solution at northern high latitude, southern middle latitude and southern high latitude, respectively.     

General aspect of GPS data use for atmospheric science

The radio link between a GPS satellite and a GPS receiver is appropriate for bistatic radar sounding of the Earth's atmosphere, ionosphere, and ocean surface (latter in case of GPS reflection). Measurements of GPS phases and amplitudes are currently performed by spaceborne, airborne, mountain- and ground-based GPS receivers. In the present paper, an uniform approach based on geometrical optics and spherical symmetry of the atmosphere is applied to various GPS observation configurations. Atmospheric mapping function, influence and retrieval of ionospheric layers/disturbances, tropospheric water vapor, and possible measurement of vertical winds and wave velocities are investigated by use of simulation data of GPS phase path excess and bending angle.     

GPS电离层反演方法研究及其在地震方面的应用

利用地基GPS数据计算了电离层单球壳模型穿刺点上的垂向总电子含量(VTEC), 根据VTEC和卫星及测站接收机的差分码间偏差DCB的不同时变特性采用了复弧法, 将VTEC作为局部变量(每30 min 一组, 可调), DCB作为一天的全局量进行解算. 在解算的过程中, 充分考虑VTEC的空间分布特性, 利用变异函数通过Kriging插值法建立电离层VTEC的二维格网模型, 并给出了卫星和接收机的差分码间偏差DCB. 通过与IGS结果的比较, 发现其结果可靠, 且时空分辨率和稳定性都有较大提高. 同时, 基于简化的三元样条插值基函数对电离层电子密度进行三维展开, 利用乘型代数重建技术MART算法构建了同批数据的四维层析成像结果, 获得了电离层电子密 度的四维分布. 其结果与CHAMP无线电掩星结果非常一致. 利用上面两种算法又分别对2008年5月长江三角洲地区地基GPS数据进行处理, 简要分析了该时段该地区上空电离层总电子含量和电子密度的变化情况及其对汶川地震的响应.      

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.     

一种基于系数择优的低阶球谐电离层延迟改正模型

针对单频接收机的电离层延迟改正问题, 提出了一种基于系数择优的低阶球谐电离层延迟改正模型. 按照电离层延迟改正模型参数择优问题的描述, 明确参数优化的目标和约束条件, 根据参数选择可编码的特点, 提出了利用遗传算法进行参数择优的方法及步骤. 以欧洲定轨中心(CODE)提供的电离层数据作为参考标准, 对参数择优模型、 低阶球谐模型和Klobuchar模型模拟的区域电离层VTEC精度进行了比较分析. 结果表明, 较之相同系数个数的低阶球谐模型, 参数择优模型精度平均改进了1～2TECU, 而且比Klobuchar模型及低阶球谐模型能更好地反映电离层的周日变化及纬度变化特征.      

Changes in total electron content (TEC) during the annular solar eclipse of 15 January 2010

The solar eclipse of 15 January 2010 was an annular eclipse of the Sun with a maximum magnitude of 0.96 at 1.62°N, 69.29°E. To study the effect of this solar eclipse on the ionosphere the GPS data recorded at three different Indian stations Varanasi (Geographic latitude 25°, 16′N, longitude 82°, 59′E), Hyderabad (Geographic latitude 17°, 20′N, longitude 78°, 30′E) and Bengaluru (Geographic latitude 12°, 58′N, longitude 77°, 33′E) have been used to retrieve ionospheric total electron content (TEC). The ionospheric response to this rare event has been studied in terms of GPS-derived TEC observed at all the three Indian stations. A significant reduction in TEC reflected by all PRNs at all the three stations has been observed. The magnitude of the reduction in VTEC compared to quiet mean VTEC depends on latitude as well as longitude. The amount of reduction observed from different satellites (PRN) is different and depends on the location of the satellite from the solar eclipse path.     

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.     

Assessment of improvement of the IRI model over Ethiopia for the modeling of the variability of TEC during the period 2013–2016

This paper discusses the monthly and seasonal variation of the total electron content (TEC) and the improvement of performance of the IRI model in estimating TEC over Ethiopia during the solar maximum (2013–2016) phase employing as reference the GPS derived TEC data inferred from four GPS receivers installed in different regions of Ethiopia; Assosa (geog 10.05°N, 34.55°E, Geom. 7.01°N), Ambo (8.97°N, 37.86°E, Geom. 5.42°N), Nazret (8.57°N, 39.29°E, Geom. 4.81°N) and Arba Minch (6.06°N, 37.56°E, Geom. 2.62°N). The results reveal that, in the years 2013–2016, the highest peak GPS-derived diurnal VTEC is observed in the March equinox in 2015 over Arba Minch station. Moreover, both the arithmetic mean GPS-derived and modelled VTEC values, generally, show maximum and minimum values in the equinoctial and June solstice months, respectively in 2014–2015. However, in 2013, the minimum and maximum arithmetic mean GPS-derived values are observed in the March equinox and December solstice, respectively. The results also show that, even though overestimation of the modelled VTEC has been observed on most of the hours, all versions of the model are generally good to estimate both the monthly and seasonal diurnal hourly VTEC values, especially in the early morning hours (00:00–03:00?UT or 03:00–06:00?LT). However, it has also been shown that the IRI 2007 and IRI 2012 versions generally perform best in matching the diurnal GPS derived TEC values as compared to that of the IRI 2016 version. In addition, the IRI 2012 version with IRI2001 option for the topside electron density shows the highest overestimation of the VTEC as compared to the other options. None of the versions of the IRI model are proved to be able to capture the effects of geomagnetic storms.     

The investigation of the ionospheric variability by the radiotranslucence method

To provide a continuous single-point sounding of a large-scale region of the ionosphere the translucence method of studying the ionosphere utilizing satellite navigation system signals has been used. Simultaneous receiving the signals of GPS Navstar and GLONASS from different azimuths gives information on variations of the ionosphere in almost real time. Using measured data the reconstruction of the electron density profiles in the regions of intersection of a sounding ray with the ionosphere has been carried out. The translucence method was used to investigate the ionosphere effects of a partial solar eclipse (PSE) that occurred on 11.08 1999 by probing of the ionosphere with different GPS system signals in the Zwenigorod region.     

Testing the improvement of performance of the IRI model in the estimation of TEC over the mid-latitude American regions

This paper mainly discusses the improvement of performance of the International Reference Ionosphere (IRI) model in estimating the variation of the Vertical Total Electron Content (VTEC) over the mid latitude American regions during the relatively low (2008–2010) and relatively high (2012) solar activity years. This has been conducted employing the VTEC values obtained from the dual frequency ground based Global Positioning System (GPS) receivers located at Mineral Area Community College, MACC (37.85°N, 269.52°W) and Mississippi County Airport, MAIR (36.85°N, 270.64°W), and the latest versions of the IRI online model (IRI 2007, IRI 2012 and IRI 2016). The study mainly focuses to compare the trend of variability of the monthly and seasonal modeled VTEC values (IRI 2007 VTEC, IRI 2012 VTEC and IRI 2016 VTEC) with the corresponding measured VTEC values (GPS VTEC). The overall results show that the IRI VTEC values (almost in all versions of the model) are generally smaller than the GPS VTEC except after about 15:00 UT (09:00 LT) in the December solstice when the Sun shifts to the high solar activity. On the contrary, overestimations of the VTEC values by the model are observed in traversing from the low solar activity (2008) to high solar activity (2012) phase, especially after about 15:00 UT (09::00 LT) with the IRI 2016 version showing the highest. In general, the IRI 2007 and IRI 2012 versions show similar monthly and seasonal underestimations or overestimations showing that the two versions have almost similar performance. The IRI 2016 version is generally better in capturing both the diurnal and arithmetic mean GPS VTEC values with some exceptional months and seasons as compared to those of the IRI 2007 and IRI 2012 versions.     

电离层周日变化对解算GPS硬件延迟稳定性的影响

针对电离层周日变化特征分析了其可能对SCORE方法估算的硬件延迟稳定性的影响. 利用BJFS以及XIAM台站的GPS观测数据, 解算了位于太阳活动高年(2001年)和太阳活动低年(2009年)的卫星硬件延迟并分析了估算的硬件延迟的稳定性. 研究发现, 电离层周日变化对估算的硬件延迟稳定性具有一定影响, 但是利用不同台站所得到的卫星硬件延迟稳定性在昼夜不同时间上的解算结果存在一定差异. 电离层周日变化对利用 BJFS台站数据解算的硬件延迟稳定性日夜差异较为明显, 在太阳活动高年利用XIAM 台站数据解算的硬件延迟日夜稳定性差异不很明显, 由于XIAM台站处于电离层赤道异常峰附近, 夜间电离层变化很大, 因此对比中纬度地区, 电离层周日变化对赤道异常峰附近地区硬件延迟稳定性解算结果的影响相对较小, 但在太阳活动低年, 其影响仍较为显著.      

New field of application of the IRI modeling – Determination of ionosphere transfer characteristic for radio astronomical signals

We suggest a new field of application of IRI modeling – determination of ionosphere transfer characteristic (ITC) for radio astronomical signals (RAS). VHF and HF RAS are widely used for observations of the Sun and pulsars. It is necessary to take into account possible distortions of RAS in the Earth ionosphere. However, in contrast to modern navigation systems (GPS, GLONASS, GALILEO), where very accurate reconstruction of ionosphere parameters is a built-in function, in present-day radio astronomy a retrieve of ITC has not been appropriately worked out yet. It collides with increasing requirements to accuracy of the analysis of RAS amplitude profile and to the angular and polarizing resolution of radio telescopes of new generation. We have developed a method and software for calculation of the ionosphere measure of rotation (RM) and the measure of dispersion (DM). We used the ionosphere model IRI-2001, magnetic-field model IGRF-10 and values of ionosphere total electron content as deduced from GPS measurements. The obtained values of the ionosphere DM and RM were recalculated into characteristics of phase delay, Faraday amplitude modulation and polarization changes. We made calculations for different levels of geomagnetic activity and for different angular position of radio sources as well.