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.     

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.     

Quality assessment of sub-Nyquist recovery from future gravity satellite missions

Drawing on experience from Gravity Recovery and Climate Experiment (GRACE) data analysis, the scientific challenges were already identified in several studies. Any future mission should focus on improvement in both precision and resolution in space and time. For future gravity missions which use high quality sensors, aliasing of high frequency time-variable geophysical signals to the lower frequency signals is one of the most serious problems. The aliasing problem and the spatio-temporal resolution are mainly restricted by two sampling theorems describing the space-time sampling of satellite missions: (i) a Heisenberg-like uncertainty theorem which states that the product of spatial resolution and time resolution is constant, and (ii) the Colombo–Nyquist rule (CNR), which requires the number of satellite revolutions in a repeat period to be at least twice a given maximum spherical harmonic degree. The CNR holds under the assumption of equal ground-track spacing, and limits the spatial resolution of the gravity solution.     

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).     

The spatio-spectral localization approach to modeling VTEC over the western part of the USA using GPS observations

The precise ionosphere modeling is crucial and remains a challenge for GPS positioning and navigation, as well as many other Earth observation systems. In this research, two approaches have been proposed to model the vertical total electron content (VTEC) of the ionosphere using spherical slepian function. For the two-dimensional case, VTEC has been modeled in a sun-fixed reference frame and the three-dimensional approach based on the system of the three-dimensional base functions has been defined as the tensor product of the spherical slepian function for the longitude and latitude in an Earth-fixed reference frame, and the polynomial B-spline function for time. Rather than the spherical harmonics, the spherical slepian functions can be employed to produce the locally and globally orthogonal bases to optimally represent the data in any arbitrary region up to a given degree. The spherical slepian functions have been applied to the real data obtained from the ground-based GPS observation across the western part of the USA.     

Quasi-biennial oscillation in GPS VTEC measurements

The quasi-biennial oscillation, QBO, a well known periodicity in the equatorial stratospheric zonal winds, is also found in ionospheric parameters and in solar and geomagnetic activity indices. Many authors speculated about the link between the QBO in solar and geomagnetic activity and the QBO in atmospheric parameters. In this work we analyze the presence of the QBO in the ionosphere using the Vertical Total Electron Content (VTEC) values obtained from Global Navigation Satellite System (GNSS) measurements during the period 1999–2012. In particular, we used IONEX files, i.e. the International GNSS Service (IGS) ionospheric products. IONEX provide VTEC values around the world at 2-h intervals. From these data we compute global and zonal averages of VTEC at different local times at mid and equatorial geomagnetic latitudes. VTEC and Extreme Ultra Violet (EUV) solar flux time series are analyzed using a wavelet multi resolution analysis. In all cases the QBO is detected among other expected periodicities.     

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.     

利用COSMIC数据构建的全球垂直TEC图的验证研究

在日固坐标系(地磁纬度和地方时)下, 累积地方时过去24h的COSMIC(Constellation Observing System for Meteorology Ionosphere andClimate)观测资料, 通过对110$sim$750km高度范围内的电子密度进行数值积分得到各掩星点的垂直TEC值, 进而利用Kriging方法插值产生近实时的全球地方时MAGLat2.5°×2h的COSMIC TEC图. 利用2008年1月1日至2010年6月30日共30个月的COSMIC数据, 逐日构建COSMICTEC图, 将其与全球导航卫星系统服务组织(International GNSS Service,IGS)发布的全球电离层TEC图(Global Ionospheric Maps, GIMs)以及OSTM/JASON-2卫星高度计观测值分别进行比对,证明利用COSMIC掩星资料构建全球电离层垂直TEC图是可行的.      

A nonlinear background removal method for seismo-ionospheric anomaly analysis under a complex solar activity scenario: A case study of the M9.0 Tohoku earthquake

A precise determination of ionospheric total electron content (TEC) anomaly variations that are likely associated with large earthquakes as observed by global positioning system (GPS) requires the elimination of the ionospheric effect from irregular solar electromagnetic radiation. In particular, revealing the seismo-ionospheric anomalies when earthquakes occurred during periods of high solar activity is of utmost importance. To overcome this constraint, a multiresolution time series processing technique based on wavelet transform applicable to global ionosphere map (GIM) TEC data was used to remove the nonlinear effect from solar radiation for the earthquake that struck Tohoku, Japan, on 11 March, 2011. As a result, it was found that the extracted TEC have a good correlation with the measured solar extreme ultraviolet flux in 26–34 nm (EUV_26–34) and the 10.7 cm solar radio flux (F_10.7). After removing the influence of solar radiation origin in GIM TEC, the analysis results show that the TEC around the forthcoming epicenter and its conjugate were significantly enhanced in the afternoon period of 8 March 2011, 3 days before the earthquake. The spatial distributions of the TEC anomalous and extreme enhancements indicate that the earthquake preparation process had brought with a TEC anomaly area of size approximately 1650 and 5700 km in the latitudinal and longitudinal directions, respectively.     

南极GPS定位中的电离层延迟分析

基于南极地区国际GNSS服务组织(IGS,International GNSS Service)跟踪站的全球定位系统(GPS,Global Position System)双频实测数据,分析了南极地区电离层延迟的变化情况及其二阶项延迟对南极GPS定位结果的影响.结果表明:南极地区的总电子含量(TEC,Total Electron Content)日间波动频繁,其日间TEC最大值变化较中纬度地区剧烈;在南极地区夏季,电离层二阶项延迟对GPS定位结果的影响可达cm级.同时,由于欧洲定轨中心(CODE,The European Center for Orbit Determination)提供的全球电离层模型(GIM,Global Ionosphere Maps)在南极区域应用的局限性,通过选取南极地区6个IGS跟踪站作为基准站建立了区域电离层TEC模型(RIM,Regional Ionosphere Model).经实测数据计算证明,对于南极地区,RIM的定位精度在一定程度上优于全球电离层模型GIM.     

Estimation of differential code biases with Jason-2/3 onboard GPS observations

With the continuous deployment of Low Earth Orbit (LEO) satellites, the estimation of differential code biases (DCBs) based on GNSS observations from LEO has gained increasing attention. Previous studies on LEO-based DCB estimation are usually using the spherical symmetry ionosphere assumption (SSIA), in which a uniform electron density is assumed in a thick shell. In this study, we propose an approach (named the SHLEO method) to simultaneously estimate the satellite and LEO onboard receiver DCBs by modeling the distribution of the global plasmaspheric total electron content (PTEC) above the satellite orbit with a spherical harmonic (SH) function. Compared to the commonly used SSIA method, the SHLEO model improves the GPS satellite DCB estimation accuracy by 13.46% and the stability by 22.34%, respectively. Compared to the GPS satellite DCBs estimated based on the Jason-3-only observations, the accuracy and monthly stability of the satellite DCBs can be improved by 14.42% and 26.8% when both Jason-2 and Jason-3 onboard observations are jointly processed. Compared with the Jason-2 solutions, the GPS satellite DCB estimates based on the fusion of Jason-2 and Jason-3 observations have an improved consistency of better than 18.26% and 9.71% with the products provided by the Center for Orbit Determination in Europe (CODE) and Chinese Academy of Sciences (CAS). Taking the DCB products provided by the German Aerospace Center (DLR) as references, there is no improvement in accuracy of the GPS satellite DCB estimates based on the fusion of Jason-2 and Jason-3 observations than the Jason-2 solutions alone. A periodic variation is found in the time series of both the Jason-3 and Jason-2 onboard receiver DCB estimates. Preliminary analysis of the PTEC distribution based on the estimated SH coefficients are also presented.     

Seismo-ionospheric anomalies in total electron content of the GIM and electron density of DEMETER before the 27 February 2010 M8.8 Chile earthquake

In this paper we examine the pre-earthquake ionospheric anomalies by the total electron content (TEC) extracted from GIM (global ionospheric map) and the electron density (Ne) observed by the DEMETER (Detection of Electro-Magnetic Emissions Transmitted from Earthquake Regions) satellite during the 2010 M8.8 Chile earthquake. Temporal variations show the nighttime TEC and Ne simultaneously increase 9–19 days before the earthquake. A cross-comparison of data recorded during the period of 1 February to 3 March in 2006–2010 confirms the above temporal anomalies specifically appear in 2010. The spatial analyses show that the anomalies tend to appear over the epicenter.     

Global empirical models of the density peak height and of the equivalent scale height for quiet conditions

Monthly average electron density profiles have been calculated from hourly electron density N(h) recorded in 26 digisonde stations distributed worldwide encompassing the time interval 1998–2006. The ionospheric electron density peak height of the F2 region, hmF2, and the effective scale height at the hmF2, Hm, deduced from average profiles have been analyzed to obtain the quiet-time behavior and have been analytically modeled by the spherical harmonic analysis (SH) technique using the modip latitude as the coordinate of the reference system. The coefficients of the SH models of hmF2 and Hm are bounded to the solar activity, and the temporal and seasonal variations are considered by Fourier expansion of the coefficients. The SH models provide a tool to predict hmF2 and Hm located anywhere in the range of latitudes between of 70°N and 70°S and at any time. The SH analytical model for hmF2 improves the fit to the observations by 10% in average compared to the IRI prediction, and it might improve the IRI prediction of hmF2 by more than 30% at high and low latitudes. The analytical model for Hm predicts the quiet behavior of the effective scale height with accuracy better than 15% in average which enables to obtain a good estimation of vertical profiles. These results could be useful to estimate information for the topside profile formulation.     

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.      

2009年1月平流层爆发性增温期间全球电离层响应的研究

2009年1月平流层爆发性增温(Stratospheric Sudden Warming, SSW)事件是有记录以来最强、持续时间最长的一次主增温事件(Major Warming Event, MWE), 期间太阳活动和地磁活动均处于较低的水平, 因此非常有利于研究电离层对平流层增温事件的响应情况. 本文利用COSMIC (Constellation Observing System for Meteorology, Ionosphere, and Climate)系统提供的掩星数据, 使用Kriging方法分别构建了此次SSW期间及平静期的电离层N_mF₂, h_mF₂和110～750km高度范围的垂直积分TEC (简称VTEC)地图, 同时从全球定位导航卫星系统服务组织(International GNSS Service, IGS)发布的全球电离层TEC地图(Global Ionospheric Maps, GIMs)中提取了日固坐标系(Sun-fixed, 地磁纬度和地方时)下全球TEC地图. 通过对比发现, SSW期间与平静期相比, 地磁纬度中低纬电离层参数存在早晨上升, 下午和夜间下降的现象. 利用OSTM/JASON-2卫星高度计观测值进行验证后的结果显示, 此前研究均未有提及的夜间时段电离层参数N_mF₂, h_mF₂和TEC (VTEC和IGS TEC)的下降现象的确存在.      

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.      

Statistical seismo-ionospheric precursors of M7.0+ earthquakes in Circum-Pacific seismic belt by GPS TEC measurements

The Circum-Pacific seismic belt is the region heavily affected by earthquakes in the world. The relationship between earthquake (e.g., the geographic location, occurrence time, magnitude, and focal depth) and ionospheric anomalies in the belt was investigated using 100 M7.0+ earthquakes during 2006–2015. The ground-based GPS measurements and global ionosphere map (GIM) data were used for the analyses of the ionospheric variations preceding the earthquakes. The results indicated that the occurrence rate of total electron content (TEC) anomalies was proportional to the magnitude and inversely proportional to the focal depth to a certain degree, and the occurrence frequency of anomalies had a rising trend with the days getting close to the main shock. The occurrence rate of TEC anomalies in the Southern hemisphere was larger than that in the Northern hemisphere. Besides, the spatial characteristics of TEC anomalies showed that the anomalies in low-middle latitudes did not coincide with the epicenter, sometimes the anomalies were also observed in the corresponding conjugated region. However, the TEC anomalies in the high latitude usually appeared around the epicenter and within the seismogenic zone while no TEC anomalies appeared in the conjugated area. These results may have potential applications to the earthquake prediction in the Circum-Pacific seismic belt.     

HASDM修正方法分析与评估

分析Jacchia70（J70）热层模式原理、美国空军高精度卫星拖曳模型（HASDM）的修正方法及选取球面调和函数的原因.推导模式密度对球谐系数（SH）的偏导数,给出利用模式密度泰勒展开进行线性化处理、迭代求解球谐系数的具体过程.针对2003年10月29日大磁暴事件,基于CHAMP和GRACE A/B卫星加速度计实测密度,进行修正方法的性能评估.统计相对误差的均值及标准差变化:改进前分别为-81.7%,74.4%;改进后分别为-5.9%,53.1%,验证了改进算法的有效性.从热层上下边界温度角度,详细分析了热层模式动态修正原理,研究结果为类HASDM修正模式的工程应用提供了理论基础.      

SHAKING: Adjusted spherical harmonics adding KrigING method for near real-time ionospheric modeling with multi-GNSS observations

Precise positioning based on Global Navigation Satellite System (GNSS) technique requires high accuracy ionospheric total electron content (TEC) correction models to account for the ionospheric path delay errors. We present an adjusted Spherical Harmonics Adding KrigING method (SHAKING) approach for regional ionospheric vertical TEC (VTEC) modeling in real time. In the proposed SHAKING method, the VTEC information over the sparse observation data area is extrapolated by the Adjusted Spherical Harmonic (ASH) function, and the boundary distortion in regional VTEC modeling is corrected by the stochastic VTEC estimated using Kriging interpolation. Using real-time GPS, GLONASS and BDS-2/3 data streams of the Crust Movement Observation Network of China (CMONOC), the SHAKING-based regional ionospheric VTEC maps are re-constructed over China and its boundary regions. Compared to GNSS VTECs derived from the independent stations, the quality of SHAKING solution improves by 13–31% and 6–33% with respect to the ASH-only solution during high and low geomagnetic periods, respectively. Compared to the inverse distance weighting (IDW) generated result, significant quality improved of SHAKING-based VTEC maps is also observed, especially over the edge areas with an improvement of 60–80%. Overall, the proposed SHAKING method exhibits notable advantage over the existing regional VTEC modeling techniques, which can be used for regional TEC modeling and associated high-precision positioning applications.