The Real-Time Working Group (RTWG) of the International GNSS Service (IGS) is
dedicated to providing high-quality data and high-accuracy products for Global
Navigation Satellite System (GNSS) positioning, navigation, timing and Earth
observations. As one part of real-time products, the IGS combined Real-Time
Global Ionosphere Map (RT-GIM) has been generated by the real-time weighting
of the RT-GIMs from IGS real-time ionosphere centers including the Chinese
Academy of Sciences (CAS), Centre National d'Etudes Spatiales (CNES),
Universitat Politècnica de Catalunya (UPC) and Wuhan University
(WHU). The performance of global vertical total electron content (VTEC)
representation in all of the RT-GIMs has been assessed by VTEC from
Jason-3 altimeter for 3 months over oceans and dSTEC-GPS technique with
2 d observations over continental regions. According to the
Jason-3 VTEC and dSTEC-GPS assessment, the real-time weighting technique is
sensitive to the accuracy of RT-GIMs. Compared with the performance of
post-processed rapid global ionosphere maps (GIMs) and IGS combined final GIM
(igsg) during the testing period, the accuracy of UPC RT-GIM (after the
improvement of the interpolation technique) and IGS combined RT-GIM (IRTG) is
equivalent to the rapid GIMs and reaches around 2.7 and 3.0 TECU (TEC unit,
1016elm-2) over
oceans and continental regions, respectively. The accuracy of CAS RT-GIM and
CNES RT-GIM is slightly worse than the rapid GIMs, while WHU RT-GIM requires a
further upgrade to obtain similar performance. In addition, a strong
response to the recent geomagnetic storms has been found in the global
electron content (GEC) of IGS RT-GIMs (especially UPC RT-GIM and IGS combined
RT-GIM). The IGS RT-GIMs turn out to be reliable sources of real-time global
VTEC information and have great potential for real-time applications including
range error correction for transionospheric radio signals, the monitoring of
space weather, and detection of natural hazards on a global scale. All the IGS
combined RT-GIMs generated and analyzed during the testing period are
available at 10.5281/zenodo.5042622.
Introduction
The global ionosphere maps (GIMs), containing vertical total electron content
(VTEC) information at given grid points (typically with a spatial resolution
of 2.5∘ in latitude and 5∘ in longitude), have been
widely used in both scientific and technological communities
. Due to the high quality and global distribution of
VTEC estimation, GIM has been applied to investigating the behavior of the
ionosphere, such as the climatology of mean total electron content (TEC),
potential ionospheric anomalies before earthquakes, semiannual variations in TEC in the
ionosphere, the VTEC structure of the polar ionosphere under different cases and
W index for ionospheric disturbance warning
e.g.,. In
addition, the high accuracy of GIM enables precise range corrections for
transionospheric radio signals including radar altimetry, radio telescopes
and Global Navigation Satellite System (GNSS) positioning
e.g.,. The
Center for Orbit Determination in Europe (CODE), European Space Agency (ESA),
Jet Propulsion Laboratory (JPL), Canadian Geodetic Survey of Natural Resources Canada (NRCan) and Universitat Politècnica de Catalunya
(UPC) agreed on the computation of individual GIMs in IONosphere map EXchange
(IONEX) format and created the Ionosphere Working Group (Iono-WG) of the
International GNSS Service (IGS) in 1998
. In
the IGS 2015 workshop, the Chinese Academy of Sciences (CAS) and Wuhan University (WHU) became
new Ionospheric Associate Analysis Centers (IAACs)
. Currently, there
are three types of post-processed IGS GIMs at different latencies: final,
rapid and predicted GIMs. With the contribution from different IAACs, the
final and rapid GIMs are assessed and combined by corresponding weights and
uploaded to File Transfer Protocol (FTP) or Hypertext Transfer Protocol (HTTP)
servers with the latency of 1–2 weeks and 1–2 d, respectively. The 1
and 2 d predicted GIMs can provide valuable VTEC information in
advance for ionospheric activities and corrections. However, the accuracy of
predicted GIMs is limited due to the nonlinear variation in ionosphere and the
lack of real-time ionospheric observations
.
In order to satisfy the growing demand for real-time GNSS positioning and
applications, the Real-Time Working Group (RTWG) of IGS was established in 2001
and officially started to provide real-time service (RTS) in 2013
. Aside from multi-GNSS real-time
data streams, the IGS-RTS also generates RT-GNSS product streams, including
satellite orbits, clocks, code/phase biases and GIM. These high-quality
IGS-RTS products enable precise GNSS positioning, navigation, timing (PNT),
ionosphere monitoring and hazard detection. In the Radio Technical Commission for
Maritime Services (RTCM) Special Committee (SC-104), the State Space
Representation (SSR) correction data format is defined as the standard message
(RTCM-SSR) for real-time GNSS applications. In support of flexible multi-GNSS
applications within current multi-constellation and multi-frequency
environments, a new format (IGS-SSR) is developed. The dissemination of IGS
Real-Time Global Ionosphere Maps (RT-GIMs) adopts spherical harmonic expansion
to save the bandwidth in both RTCM-SSR and IGS-SSR formats
.
The accuracy of RT-GIMs is typically worse than post-processed GIMs due to the
short span of ionospheric observations, sparse distribution of stations,
higher noises in carrier-to-code leveling, or difficulty in carrier ambiguity
estimation in real-time processing mode. While RT-GIMs perform slightly worse
than post-processed GIMs, it is found that RT-GIMs are helpful to reduce the
convergence time of dual-frequency precise point positioning (PPP), and they
strengthen the solution . With the corrections of RT-GIMs,
the accuracy of single-frequency PPP reaches decimeter and meter level in
horizontal and vertical directions , while the
instantaneous (single-epoch) real-time kinematic (RTK) positioning over medium
and long baselines is able to obtain a higher success rate of the ambiguity
fixing and reliability for rover stations at a level of a few centimeters
. In addition, the feasibility of ionospheric
storm monitoring based on RT-GIMs is tested . A first
fusion of IGS-GIMs and ionosonde data from the Global Ionosphere Radio
Observatory (GIRO) paves the way for the improvement of real-time
International Reference Ionosphere . Currently, the
routine RT-GIMs are available from CAS, Centre National d'Etudes Spatiales
(CNES), German Aerospace Center in Neustrelitz (DLR-NZ), JPL, UPC, WHU and
IONOLAB
. Individual
RT-GIMs from different IGS centers can be gathered from IGS-RTS by means of
Network Transportation of RTCM by Internet Protocol (NTRIP)
. With the contribution of IGS RT-GIMs from CAS, CNES and
UPC, a first IGS real-time combination of GIMs was generated in 2018
.
Recently, one of the IGS RT-GIMs (UPC-IonSAT) has completely changed the
real-time interpolation strategy, with a significant improvement. In addition,
the number of contributing centers has been increased from three to four, thanks to
the participation of Wuhan University. A new version of IGS combined RT-GIM
(IRTG) has been developed to improve the performance and also adapt to the
newly updated IGS-SSR format. In addition, the developed software has been
further parallelized to decrease the latency of IRTG computation to a few
minutes . This paper summarizes the computation methods of
IGS RT-GIMs from different ionosphere centers and the generation of IRTG. In
addition, the performance of different RT-GIMs and the real-time weighting
technique is shown and discussed. The conclusions and future improvements are
given in the final section.
Data and methodsReal-time GNSS data processing
In order to generate RT-GIMs, the real-time GNSS observations from worldwide
stations are received and transformed into slant TEC (STEC). It should be
noted that extraction of STEC in an unbiased way can be obtained by fitting an
ionospheric model to the observations. With the global distributed STEC,
different strategies are chosen for the computation of RT-GIMs.
Currently, two methods are commonly used for the calculation of real-time
STEC. The first method is the so-called carrier-to-code leveling (CCL) as
shown in Eq. ()
. The geometry-free (GF) combination
of pseudorange and carrier phase observations is formed to extract STEC and
differential
code bias (DCB) in an unbiased way by fitting an ionospheric model (for example, spherical
harmonic model). Due to the typically shorter phase-arc length in real-time
mode, the impact of multipath and thermal noise is higher than in
post-processing mode .
PGF,t≡P2,t-P1,t1=αGF⋅STECt+c⋅(Dr+Ds)+ϵM+ϵT2LGF,t≡L1,t-L2,t=αGF⋅STECt+BGFP̃GF,t≡LGF,t-1k∑i=1kLGF,i-PGF,i3≈αGF⋅STECt+c⋅(Dr+Ds)
Here P1,t and P2,t are the pseudorange observations of epoch t at
first and second frequencies, respectively. αGF can be
approximated as 40.3(1f22-1f12). f1 and
f2 are the first and second frequencies of observation. STECt is the STEC
of epoch t. r is receiver and s is satellite. c is the speed of light
in vacuum. Dr and Ds are the receiver differential
code biases (DCBs) and satellite DCB. ϵM and
ϵT are the code multipath error and thermal noise
error. L1,t and L2,t are the carrier phase observations including
the priori corrections (such as wind-up term) of epoch t at first and second
frequencies. BGF equals B1-B2, while B1 and B2 are the
carrier phase ambiguities including the corresponding phase bias at first and
second frequencies, respectively. k is the length of smoothing arc from
beginning epoch to epoch t, and P̃GF,t represents the smoothed
PGF of epoch t, which is significantly affected by the
pseudorange multipath in real-time mode than in post-processing.
The brief summary of different IGS RT-GIMs.
Agency/GIMRunning dateExtra ionospheric informationDCB computationGIM computationCASMid-2017 to present2 d predicted GIM as background informationEstimated at the same time with local VTEC, and corrected by 3 d aligned code biasObservations with predicted GIMs generate 15∘ spherical harmonic expansion GIM in solar-geographic frameCNESEnd of 2014 topresent (with an evolution of the spherical harmonic degree)NoExpected in a forthcoming version12∘ spherical harmonic expansion GIM which is generated in solar-geographic frameUPC/URTG6 Feb 2011 to8 Sep 20191–2 d rapid GIM UQRG as background informationOptionalTomographic model with kriging interpolation method and frozen rapid GIM (UQRG) as a priori model, which generates RT-GIM in sun-fixed geomagnetic frameUPC/USRG8 Sep 2019 to present1–2 d rapid GIM UQRG as background informationOptionalTomographic model with spherical harmonic interpolation method and frozen rapid GIM (UQRG) as a priori model, which generates RT-GIM in sun-fixed geomagnetic frameUPC/UADG4 Jan 2021 to presentHistorical UQRG (since 1996) as databasesOptionalTomographic model adoptingatomic decomposition and LASSO solution for the global interpolation with the help of historical GIMs (UQRG), which generates GIM in sun-fixed geomagnetic frameWHU9 Nov 2020 to present2 d predicted GIM as background informationDirectly use the previoussatellite and receiver DCB estimated simultaneouslywith WHU rapid GIMObservations with predicted GIMs yield 15∘ spherical harmonic expansion GIM in solar-geomagnetic frame
The second method is the GF combination of phase-only observations, and the
BGF is estimated together with the real-time TEC model (for
example, described in terms of tomographic voxel-based basis functions) in
Eq. () . Although the
STEC from the second method is accurate and free of code multipath and thermal
noise in post-processing, the convergence time can affect the accuracy of the
STEC, most likely in the isolated receivers. In addition, the computation
methods of RT-GIMs from different IGS real-time ionosphere centers were
compared in detail at the next subsection and summarized in
Table . Some ionosphere centers (CAS, CNES, WHU)
directly estimate and disseminate spherical harmonic coefficients in a sun-fixed
reference frame as Eq. ()
, while UPC generates the RT-GIM in IONEX format
and transforms RT-GIM into spherical harmonic coefficients for the
dissemination.
Mz=1-sin2z/(1+Hion/RE)2-12VTECt=STECt/MzVTECt=∑n=0NSH∑m=0min(n,MSH)Pn,m(sinφI)⋅(Cn,mcos(mλS,t)+Sn,msin(mλS,t))λS,t=(λI+(t-t0)×π/43200) modulo 2π
Here z is the satellite zenith angle, and Mz is the mapping function between
STECt and VTECt. Hion is the height of the ionospheric
single-layer assumption, and RE is the radius of the
earth. VTECt is the VTEC of epoch t. NSH is the max degree of
spherical harmonic expansion, and MSH is the max order of
spherical harmonic expansion. n and m are corresponding indices. Pn,m is
the normalized associated Legendre functions. Cn,m and Sn,m are
sine and cosine spherical harmonic coefficients. φI and
λI are the geocentric latitude and longitude of
ionospheric pierce point (IPP). λS,t is the mean sun fixed
and phase-shifted longitude of IPP of epoch t (typically shifted by
2 h to approximate TEC maximum at 14:00 LT). t is the current
epoch. t0 is a common reference of shifted hours, taken as 0 h in
the present broadcasting of RT-GIM for WHU and 2 h for CAS, CNES and
UPC.
The computation of RT-GIMs by different IGS real-time
ionosphere centers
The strategies for generating RT-GIMs differ between IGS real-time ionospheric
analysis centers (ACs). In this subsection, a brief introduction on the
generation of RT-GIMs from individual ACs and the strategy comparison
between different ACs are given.
Chinese Academy of Sciences
The post-processed GIM of CAS has been computed and uploaded to IGS since 2015
. A predicting-plus-modeling approach is used by CAS for
the computation of RT-GIM . CAS RT-GIM is generated with
multi-GNSS, GPS and GLONASS L1 + L2, BeiDou B1 + B2, and Galileo E1 + E5a real-time
data streams, provided by the IGS and regional GNSS tracking network
stations. The real-time DCBs are estimated as part of the local ionospheric
VTEC modeling using a generalized trigonometric series (GTS) function as
Eq. (). Then 3 d aligned biases are incorporated to
increase the robustness of real-time DCBs .
STECt=Mz⋅VTECt+c⋅Ds+DrVTECt=∑i=0imax∑j=0jmaxEi,j⋅φdi⋅λdj+∑l=0lmaxClcos(l⋅ht)+Slsin(l⋅ht)ht=2π(t-14)/T,T=24himax=jmax=2lmax=4
Here r is receiver and s is satellite. φd and λd are the difference between IPP and station in latitude
and longitude, respectively. i,j and l represent the degrees in the polynomial
model and Fourier series expansion. Ei,j,Cl and Sl are unknown
parameters.
The real-time STEC is computed by subtracting estimated DCB in
Eq. () from P̃GF,t in Eq. (), and
then the STEC is converted into VTEC by means of a mapping function. The
real-time VTEC from 130 global stations is directly modeled in a
solar-geographic reference frame as Eq. (). To mitigate
the impacts of the unstable real-time data streams, e.g., the sudden
interruption of the data streams, CAS-predicted TEC information is also
included for RT-GIM computation. The broadcasted CAS RT-GIM is computed by the
weighted combination of real-time VTEC spherical harmonic coefficients and
predicted ionospheric information .
Centre National d'Etudes Spatiales
In the framework of the RTS of the IGS, CNES has computed global VTEC in real time
thanks to the CNES PPP-WIZARD project since 2014. The real-time VTEC is
extracted by pseudorange and carrier phase GF combination as
Eq. () with the help of a mapping function. The
single-layer assumption in the mapping function adopts an altitude of
450 km above the Earth.
CNES also uses a spherical harmonic model for global VTEC representation, and the
equation is the same as Eq. (). Spherical harmonic
coefficients are computed by means of a Kalman filter and simultaneous STEC
from 100 stations of the real-time IGS network. CNES started to broadcast
RT-GIM at the end of 2014 and changed spherical harmonic degrees from 6 to 12
in May of 2017 .
Universitat Politècnica de Catalunya
UPC has been providing daily GIMs in IONEX format to IGS since 1998
. In order to
meet the demand of real-time GIM, the second author of this paper (from UPC-IonSAT) developed the Real-Time TOMographic
IONosphere model software (RT-TOMION) and started to generate the UPC RT-GIM
on 6 February 2011. The phase-only GF combination as Eq. () is
used for obtaining real-time STEC from around 260 stations, and a 4-D
voxel-based tomographic ionosphere model is adopted for global electron
content modeling. The ionosphere is divided into two layers in the tomographic
model, and the electron density of each voxel is estimated together with the
ambiguity term BGF by means of a Kalman filter in the sun-fixed
reference frame. The estimated electron density is condensed at a fixed
effective height (450 km) for the generation of a single-layer VTEC
map, and then the VTEC interpolation method is adopted in a sun-fixed
geomagnetic reference frame for filling the data gap on a global scale.
From 2011 to 2019, the kriging technique is selected by UPC for real-time VTEC
interpolation. And the spherical harmonic model has been adopted by UPC since
8 September 2019. Recently, a new interpolation technique, denoted atomic
decomposition interpolator of GIMs (ADIGIM), was developed. Since the
global ionospheric electron content mainly depends on the diurnal, seasonal
and solar variation, ADIGIM is computed by the weighted combination of
good-quality historical GIMs (e.g., UQRG) with similar ionosphere
conditions. The database of historical GIMs covers the last two solar cycles
since 1998. The method for obtaining the weights of the linear combination of
past maps is based on Eq. (), which was first introduced in
the problem of face recognition
. While the face recognition is
affected by the occlusions (such as glasses) in the face image, the
reconstruction of GIM has problems in the regions that are not covered by
GNSS stations. The problems have to be taken into account when selecting the
past maps for combination and should not introduce a bias. As shown in
Eq. (), the problem is solved by introducing ℓ2 norm
and ℓ1 norm. The property of the atomic decomposition and the least
absolute shrinkage and selection operator (LASSO) is that it can select a
small set of past maps which are the most similar to the real-time-measured
VTEC at IPPs. The ADIGIM technique minimizes the difference between observed
VTEC measurement and weighted VTEC from historical UQRG in similar ionosphere
conditions. The underlying assumption is that the VTEC distribution over the
areas not covered by the IPPs can be represented by the elements of the
historical library of UQRG . The UPC RT-GIM with the new
technique is denoted as UADG and generated by Eq. (). Due to
the improvement provided by the UADG, the broadcasted UPC-GIM was changed from
USRG to UADG on 4 January 2021. In addition, the USRG and UADG are generated
in real-time mode and saved in IONEX format at HTTP as shown in
Table .
VTECI,t≈Dg,I,t⋅αtα̃t=argminαt12VTECI,t-Dg,I,t⋅αtℓ2+ραtℓ1Gt=Dtα̃t
Here VTECI,t is the observed VTEC at IPP of epoch
t. It is assumed that VTECI,t can be approximated by
Dg,I,t and αt, while Dg,I,t is the VTEC
extracted at IPP from historical databases of GIM g (for UPC, the UQRG is
used), and αt is the unknown weight vector of each historical GIM at
epoch t. α̃t is the estimated weight vector of each
selected UQRG at epoch t. The estimated weight vector α̃t
is obtained by the LASSO regression method with loss function norm ℓ2 and
regularization norm ℓ1. ℓ2 is the norm for minimizing the
Euclidean distance between observed VTEC measurements and historical UQRG
databases at epoch t. ℓ1 is the regularization norm for penalizing
the approximation coefficients to limit the number of UQRG involved in the
estimation, and ρ controls the sparsity of solution. Gt is the
generated UPC RT-GIM of epoch t and is the weighted combination of
historical UQRG. For mathematical convenience, each 2-D GIM is reformed as a
1-D vector (i.e., the columns are stacked along the meridian in order to
create a vector of all the grid points of the map). This is justified because
the measure of similarity is done over cells of 2.5∘×5.0∘
in the maps, and therefore the underlying R2 (coordinate space of
dimension 2) structure is not relevant for computing Euclidean distances in
ℓ2 norm. Dt is the selected historical UQRG database with
similar ionosphere conditions at epoch t.
Wuhan University
The daily rapid and final GIM products have been generated with new WHU
software named GNSS Ionosphere Monitoring and Analysis Software (GIMAS) since
21 June 2018 . At the end of the year 2020, WHU
also published a first RT-GIM product.
WHU uses the spherical harmonic expansion model, and the formula is identical
to Eq. (). Currently, only the GPS real-time data
streams from about 120 globally distributed IGS stations are used. The double-frequency code and carrier phase observations with a cut-off angle of
10∘ are used to gather precise geometry-free ionospheric data
with the CCL method as Eq. () and ionospheric mapping
function with the layer height of 450 km. In order to avoid the
influence of satellite and receiver DCB on ionospheric parameter estimation,
WHU directly uses the previous estimated DCB from the WHU rapid GIM
product. According to previous experience, the real-time data are not enough to
model the ionosphere precisely on a global scale with the spherical harmonic
expansion technique. Considering the lack and the uneven distribution of the
GPS-derived ionospheric data, 2 d predicted GIM as external
ionospheric information is also incorporated. It is important to balance the
weight between the real-time data and the background information. Both the
RT-GIM quality and the root mean square (rms) map are influenced by the weight
.
In the year 2021, WHU is going to focus on how to further improve the accuracy
of RT-GIM and update the computation method. The precise WHU RT-GIMs with
multi-GNSS data and the application of WHU RT-GIM in the GNSS positioning as
well as space physics domain are expected as next steps.
The combination of IGS RT-GIMs
Thanks to the contribution of the initial IGS real-time ionosphere centers
(CAS, CNES and UPC) and globally distributed real-time GNSS stations, the
first experimental IRTG was generated by means of the real-time dSTEC (RT-dSTEC)
weighting technique (normalized inverse of the squared rms of RT-dSTEC error)
in October 2018 . Recently, WHU published the first
WHU RT-GIM, and UPC upgraded the real-time VTEC interpolation technique. A new
version of IRTG has been developed and broadcasted since 4 January 2021. The
IGS combined RT-GIM is based on the weighted mean value of VTEC from different
IGS centers as Eq. ().
VTECIRTG,t=∑g=1NAC(wg,t⋅VTECg,t)wg,t=Ig,t/∑g=1NAC(Ig,t)Ig,t=1/RMSδ,g,t2RMSδ,g,t=∑i=1Nt(δg,i)2/Nt
Here VTECIRTG,t is the VTEC of IGS combined RT-GIM at
epoch t, and VTECg,t is VTEC of RT-GIM g from the IGS center at
epoch t. NAC is the number of IGS centers. wg,t is the
weight of corresponding RT-GIM g at epoch t (the sum of wg,t at epoch
t is 1). RMSδ,g,t is the root mean square of RT-dSTEC error at
epoch t. Ig,t is the inverse of the mean square of RT-dSTEC error at
epoch t. Nt is the number of RT-dSTEC observations from the beginning
epoch to the current epoch t. δg,i is the RT-dSTEC error of
RT-GIM g in the RT-dSTEC assessment.
In addition, the RT-dSTEC assessment is based on root mean square (rms) of the
dSTEC error calculated by Eq. (). In order to adapt to the
real-time processing mode, the ambiguous reference STEC measurement
LGF,tref is set to be the first elevation angle higher than
10∘ within a continuous phase arc to enable the RT-dSTEC calculation in
the elevation-ascending arc.
δg,t=1αGF((LGF,t-LGF,tref)8-(Mz⋅VTECg,t-Mzref⋅VTECg,tref)),
where δg,t is the dSTEC error of GIM g at epoch
t. tref is the epoch when reference elevation angle is
stored. Mz and Mzref are the mapping functions of zenith
angle of epoch t and zenith angle of reference epoch tref,
respectively.
The current status of broadcasting IGS RT-GIMs.
AgencyTemporalBroadcastSphericalMount pointsReal-time IONEXresolutionfrequencyharmonicin NTRIP castersaved at FTP/HTTPdegreeCAS5 min1 min15123.56.176.228:2101/CAS05a 59.110.42.14:2101/SSRA00CAS1b 59.110.42.14:2101/SSRA00CAS0a 59.110.42.14:2101/SSRC00CAS1b 59.110.42.14:2101/SSRC00CAS0a 182.92.166.182:2101/IONO00CAS1b 182.92.166.182:2101/IONO00CAS0aftp://ftp.gipp.org.cn/product/ionex/ (last access: 10 September 2021) (update at the end of day)CNES2 min1 min12products.igs-ip.net:2101/CLK91a products.igs-ip.net:2101/SSRA00CNE1b products.igs-ip.net:2101/SSRA00CNE0a products.igs-ip.net:2101/SSRC00CNE1b products.igs-ip.net:2101/SSRC00CNE0aNoUPC (only UADG)15 min15 s15products.igs-ip.net:2101/IONO00UPC1bhttp://chapman.upc.es/tomion/real-time/quick/ (last access:10 September 2021) (UADG and USRG,update every 15 min)WHU5 min1 min1558.49.58.150:2106/IONO00WHU0aNoIGS20 min15 s15products.igs-ip.net:2101/IONO00IGS1bhttp://chapman.upc.es/irtg/ (last access:10 September 2021) (update every 20 min)
a RTCM-SSR format.b IGS-SSR format.
The 25 common real-time stations for RT-dSTEC assessment (in green) and 50 external GNSS stations for dSTEC-GPS assessment (in red).
Data flow for the IGS real-time combined GIM.
Due to the limited number of real-time stations, 25 common real-time stations
that have been used by all the IGS real-time ionosphere centers are selected
for allowing a fair RT-dSTEC assessment. The distribution can be seen as
Fig. . Therefore, the RT-dSTEC is the measurement of
“internal” post-fit residuals of RT-GIMs and still sensitive to the
accuracy of assessed GIMs. Every 20 min, the RT-dSTEC assessment is
performed and used for the combination of different IGS RT-GIMs. The steps for
the generation of IRTG can be seen as Fig. . The RTCM-SSR has
been the standard message for real-time corrections, and the IGS State Space
Representation (SSR) format version 1.00 was published on 5 October 2020
. The content of IGS-SSR is compatible with RTCM-SSR
contents. And the IGS-SSR format can support more extensions such as satellite
attitude, phase center offsets, and variations in the near future. At present,
both RTCM-SSR and IGS-SSR formats are used for the dissemination of
RT-GIMs. In addition, IGS defines different references for antenna correction:
average phase center (APC) and center of mass (CoM). The current status of
RT-GIMs from different ionosphere centers can be seen in
Table . It should be noted that “SSRA” means the SSR
with the APC reference, and “SSRC” means the SSR with the CoM reference.
The performance of IGS RT-GIMs
In this section, the performance of IGS RT-GIMs was analyzed and compared
with rapid IGS GIMs as well as IGS combined final GIM. It should be noted that
the RT-GIMs were gathered with BKG Ntrip Client (BNC) software
and generated by received spherical harmonic coefficients
from different centers as in Table . And there were two
kinds of temporal resolution for received RT-GIMs: the common temporal
resolution of 20 min and the full (original) temporal
resolution. Since the IRTG is combined every 20 min, we will focus on
such a common time resolution to compare the performance. The detail of
compared RT-GIMs can be seen in Table . The influence of
temporal resolution on RT-GIMs was also shown in this section.
The ID of compared IGS RT-GIMs.
Agency20 min RT-GIMRT-GIM with fulltemporal resolutionCAScrtgcrfgCNEScnescnfsUPCupc1upf1WHUwhu0whf0IGSirtgirfg*
* Note irfg and irtg are the same.
Before detailing the Jason-3 VTEC and GPS-dSTEC assessment, it should be taken
into account that the GIM error versus Jason VTEC measurements have a high
correlation with the GIM error versus dSTEC-GPS measurements, although
the Jason VTEC measurements are vertical and the dSTEC-GPS measurements are
slanted. As demonstrated in , the Jason-3 VTEC
assessment and dSTEC-GPS assessment are independent and consistent for GIM
evaluation. In other words, the slant ray path geometry changes do not
affect the capability of dSTEC reference data to rank the GIM, and the
electron content between the Jason-3 altimeter and the GNSS satellites does not
significantly affect the assessment of GIMs based on Jason-3 VTEC data.
Jason-3 VTEC assessment
The VTEC from the Jason-3 altimeter was gathered as an external reference over
the oceans. After applying a sliding window of 16 s to smooth the
altimeter measurements, the typical standard deviation of Jason-3 VTEC
measurement error is around 1 TECU. Although the electron content above the
Jason-3 altimeter (about 1300 km) is not available and the altimeter
bias is around a few TECU, the standard deviation of the difference between
GIM-VTEC and Jason-3 VTEC is adopted to avoid the Jason-3 altimeter bias and the
constant bias component of the plasmaspheric electron content in the
assessment. The plasmaspheric electron content variation is up to a few TECU
and is a relatively small part when compared with the GIM errors over the
oceans. Jason-3 VTEC has been proven to be a reliable reference of VTEC over
the oceans. The oceans are the most challenging regions for GIMs where
permanent GNSS receivers are typically far away
. In this context, the
daily standard deviation of the difference between Jason-3 VTEC and GIM-VTEC
was suitable as the statistic for GIM assessment in
Eq. ().
Biasg=∑i=1NJ(VTECJason-3,i-VTECg,i)/NJSTDg=∑i=1NJ(VTECJason-3,i-VTECg,i-Biasg)2/(NJ-1),
where VTECJason,i and VTECGIM,i are VTEC
extracted from Jason-3 and GIM observation i, respectively. NJ is the
number of involved observations.
The recent 3-month data (1 December 2020 to 1 March 2021), containing the
two significant events (new contributing RT-GIM (WHU) from 3 January 2021 and
the introduction of the new atomic decomposition UPC-GIM (UADG) on
4 January 2021), have been selected to study the consistency and performance of
the IGS RT-GIMs.
As can be seen in Fig. , the standard deviation of UPC
RT-GIM (upc1) VTEC versus measured Jason-3 VTEC is worse than other RT-GIMs
before the transition from USRG to UADG on 4 January 2021. It should be noted
that the upc1 in RTCM-SSR format was stopped from 15 December 2020 to
2 January 2021, due to the change of broadcasting format and some technical
issues. The assessment of upc1 was based on the UPC RT-GIMs saved in a local
repository during the interrupted period. The standard deviation of upc1 VTEC
versus measured Jason-3 VTEC reached around 7 TECU on 6 December 2020 due to
the interruption of the downloading module. And the upc1 achieved a significant
improvement after the transition on 4 January 2021. In addition, the accuracy
of IGS experimental combined RT-GIM (irtg) also increased due to the better
performance of upc1. Compared with IGS rapid GIMs (corg, ehrg, emrg, esrg,
igrg, jprg, uhrg, uprg, uqrg, whrg) and IGS final combined GIM (igsg), the
upc1 and irtg are equivalent to the post-processed GIMs and even better than
some rapid GIMs. The accuracy of CAS RT-GIM (crtg) and CNES RT-GIM (cnes) is
close to the post-processed GIMs, while WHU RT-GIM (whu0) is slightly worse
than the other GIMs. As shown and explained in Eq. (),
the whu0 is shifted by 0 h. To see the influence of phase-shifted
λS,t, the whu0 is manually shifted by 2 h (i.e.,
take t0 as 2 h for whu0 in Eq. ) in
post-processing mode. And the accuracy of the 2 h shifted WHU RT-GIM
(whu1) is slightly better than whu0 as can be seen in
Fig. .
Daily standard deviation of GIM VTEC versus measured Jason-3 VTEC (in TECU), from 1 December 2020 to 1 March 2021.
Standard deviation of GIM-VTEC minus Jason-3 VTEC in Jason-3 VTEC assessment (last two columns) and dSTEC-GPS assessment results of RT-GIMs on 3 January (second and third columns) and 5 January (fourth and fifth columns) in 2021.
GIMRMSE of3 January indSTEC-GPSassessment (TECU)Relative error of3 January indSTEC-GPSassessment (%)RMSE of5 January indSTEC-GPSassessment (TECU)Relative errorof 5 Januaryin dSTEC-GPSassessment (%)Overall standarddeviation of theGIM-VTEC versus measuredJason-3 VTECfrom 1 December2020 to 3 January2021 in Jason-3VTEC assessment (TECU)Overall standarddeviation ofGIM-VTEC versus measuredJason-3 VTECfrom 4 Januaryto 1 March 2021in Jason-3 VTECassessment (TECU)corg2.9045.073.3549.203.12.9ehrg2.5439.552.8141.233.02.8emrg2.6240.752.7340.083.22.9esrg2.7041.983.0644.993.23.0igrg2.6040.403.0644.992.92.8jprg2.7342.462.8641.982.82.7uhrg1.9129.692.2132.433.92.8uprg2.0431.802.4135.393.92.8uqrg1.8929.442.1932.243.52.8whrg2.4237.632.6538.943.02.8igsg2.3336.252.5737.742.62.5crtg3.3652.253.8656.673.63.2crfg4.2966.673.9257.563.73.2cnes3.3552.133.7454.863.53.4cnfs3.5855.734.6267.883.53.4upc13.8559.912.8041.064.32.7upf13.8760.202.8141.264.52.7whu05.1980.695.4579.844.34.4whf05.3182.615.5481.284.34.4whu14.3767.974.4064.554.33.8irtg4.1163.863.3749.473.32.8
The value in bold font means the corresponding RT-GIM has the best
performance among the remaining RT-GIMs in each column, and values of irtg are
italic for comparison.
In order to investigate the influence of temporal resolution on RT-GIMs over
oceans, different RT-GIMs with full temporal resolution were involved. The
summary of Jason-3 VTEC assessment can be seen in
Table . The overall standard deviation of GIM-VTEC
minus Jason-3 VTEC is computed in separate time periods to focus on the
influence of the transition from USRG to UADG. As shown in
Table , the overall standard deviation of GIM-VTEC
versus Jason-3 VTEC is consistent with Fig. , and the
quality of 20 min and full temporal resolution of RT-GIMs are similar
over oceans. And the accuracy of 2 h shifted whu1 in Jason-3 VTEC
assessment is higher than whu0 in Table . In
particular, the overall standard deviation of upc1 VTEC versus measured
Jason-3 VTEC drops from 4.3 to 2.7 TECU, and, in agreement with that, the
standard deviation of irtg VTEC versus measured Jason-3 VTEC decreases from 3.3
to 2.8 TECU.
dSTEC-GPS assessment
In addition, dSTEC-GPS assessment in post-processing mode was involved as a
complementary tool with high accuracy (better than 0.1 TECU) over continental
regions on a global scale. In the dSTEC-GPS assessment, the maximum elevation
angle within a continuous arc was regarded as the reference angle in
Eq. (). The dSTEC observations provide the direct measurements
of the difference of STEC within a continuous phase arc involving different
geometries. As has been introduced before, the STEC is proportional to VTEC
by means of the ionospheric mapping function. Therefore, the dSTEC error
observations (see Eq. ), containing different geometries and
mapping function error are direct measurements for evaluating GIM-STEC, which
is commonly used by GNSS users to calculate ionospheric correction. In
addition, the common agreed ionospheric thin layer model is set to be
450 km in height in the generation of GIM to provide VTEC in a consistent
way for different ionospheric analysis centers. And in this way the GNSS users
are able to consistently recover the STEC from GIM-VTEC by the
commonly agreed mapping function. The dSTEC-GPS assessment was performed by
globally distributed GNSS stations as shown in Fig. on
3 January (before the transition of UPC RT-GIM from USRG to UADG) and
5 January (after the transition) in 2021, with a focus on the transition of
UPC RT-GIM. The rms error and relative error were used for the assessment as
Eq. ().
RMSδ,g=∑i=1NS(δg,i)2/NSOΔSGPS,t,i=(LGF,t-LGF,tref)/αGFRMSΔSGPS=∑i=1NS(OΔSGPS,t,i)2/NSRelative errorg=100⋅RMSδ,g/RMSΔSGPS
Here RMSδ,g is the rms error of GIM g. And δg,i
is the dSTEC error of GIM g similar to Eq. (), while the
reference angle of Eq. () is replaced by the maximum elevation
angle within a continuous arc. NS is the number of involved
observations. OΔSGPS,t,i is the dSTEC-GPS
observation. RMSΔSGPS is the rms of the observed
dSTEC-GPS. Relative errorg is the relative error of GIM g.
The distribution of dSTEC-GPS results on 5 January 2021 (after the improvement of the UPC interpolation technique).
As shown in Table , the rms error of most
post-processed GIMs reaches around 2 or 3 TECU, while the rms error ranges
from 2.8 to 5.54 TECU for RT-GIMs. The transition of UPC RT-GIM (upf1) from
USRG to UADG is apparent in the dSTEC-GPS assessment, and the rms error of IGS
RT-GIM (irtg) decreased from 4.11 to 3.37 TECU due to the improvement of UPC
RT-GIM. After the transition of UPC RT-GIM, the performance of upf1 and irtg
is comparable with most post-processed GIMs. Similar to the performance in the
Jason-3 VTEC assessment, the accuracy of the remaining RT-GIMs is close to
post-processed GIMs. And the rms error of 2 h shifted whu1 is around
4.4 TECU, which is better than the whu0. Therefore, the 2 h shift is
recommended for λS,t in Eq. (). It
should be pointed out that the performance of RT-GIMs with the full temporal
resolution is slightly worse than 20 min RT-GIMs. Furthermore, the
full temporal resolution RT-GIM is even worse than the GIM obtained by linear
interpolation of the 20 min RT-GIM in a sun-fixed reference
frame. This is coincident with a smaller number of ionospheric observations at
shorter timescales. In Fig. , the performance of
IGS RT-GIMs after the upgrade of the UPC interpolation method in the dSTEC-GPS
assessment is represented. The higher values of rms errors occur around the
Equator and Southern Hemisphere for all the RT-GIMs. And the higher values
might be caused by the high-electron-density gradients at the Equator and the
sparse distribution of real-time stations in the Southern Hemisphere.
The sensibility of real-time weighting technique
RT-dSTEC assessment of RT-GIMs was automatically running in real-time mode
and used for real-time weighting in the combination of IGS RT-GIMs. In order
to compare with the dSTEC-GPS assessment, the RT-dSTEC assessment with
real-time stations in Fig. was also performed on 3 and
5 January 2021. As can be seen in Table , the rank
of RT-GIMs in the RT-dSTEC assessment is similar to the dSTEC-GPS assessment, but the
rms error values are larger. And the larger rms error coincides with the
much lower elevation angle of the observation reference in the RT-dSTEC
assessment.
RMSE of RT-GIMs in RT-dSTEC assessment on 3 and 5 January 2021.
GIMRMSE ofRMSE of3 January (TECU)5 January (TECU)upc14.243.91crtg4.254.98cnes3.984.07whu05.945.81
The value in bold font means the corresponding RT-GIM has the best performance among the remaining RT-GIMs in each column.
The evolution of real-time weights and daily winning epochs of RT-GIMs. (a) The real-time weights from 3 to 5 January 2021. (b) The daily number of epochs when one of the RT-GIMs is better than the others from 1 December 2020 to 1 March 2021.
The GEC, ap and Dst evolution of RT-GIMs from 24 to 29 January 2021 during the low-solar-activity period.
The real-time weights of RT-GIMs can be defined as the normalized inverse of
the squared rms of RT-dSTEC errors and represent the accuracy of RT-GIMs in
the RT-dSTEC assessment. For each RT-GIM, the number of daily winning epochs
is computed by counting the number of epochs within the day when the one
RT-GIM is better than the other RT-GIMs. The evolution of daily winning epochs
of RT-GIMs shown in the bottom figure of Fig. is consistent
with the Jason-3 VTEC assessment. The upc1 was not involved in the combination
from 15 December 2020 to 2 January 2021 when the dissemination of upc1 was
stopped, as can be seen in the bottom figure of Fig. . The
significant improvement of the transition of upc1 from USRG to UADG shown in
dSTEC-GPS and the Jason-3 VTEC assessment is also obvious in the top panel of
Fig. . In addition, the daily winning epoch's evolution and the
transition in Fig. are consistent with the accuracy of
RT-GIMs, providing a combined RT-GIM which is one of the best RT-GIMs, as shown
in the altimeter-based and dSTEC-based assessments. The good performance of
the combination algorithm can be mainly explained from the point of view of
the weights, i.e., the sensitivity of the dSTEC error to the quality of the
RT-GIMs, but also from the point of view of the linear combination that can
play a positive role under any potential negative correlation between the
performance of pairs of involved RT-GIMs.
The response of RT-GIMs to recent minor geomagnetic storms
The global electron content (GEC) is defined as the total number of free
electrons in the ionosphere. Hence the GEC can be estimated from the summation
of the product of the VTEC value and the area of the corresponding GIM
cell. In addition, GEC has been used as an ionospheric index
. With the purpose of further
checking the consistency of IGS RT-GIMs, the GEC of RT-GIMs was calculated and
compared from 24 to 29 January 2021. It should be noted that the solar
activity is low in January 2021. During the selected period, several weak
geomagnetic storms and one moderate geomagnetic storm occurred according to
the classification of geomagnetic indices
, and the GEC
evolution can be seen in Fig. . The GEC of CNES RT-GIM (cnfs) is
slightly different from other RT-GIMs, and seems to be caused by the bias in
CNES RT-GIM. There are some jumps in the GEC evolution of CAS RT-GIM (crfg)
and WHU RT-GIM (whf0), and the jumps might be related to the handling of day
boundary or unreal predicted GIM in certain cases. Compared with IGS final
combined GIM (igsg), the good performance of global VTEC representation with
upf1 and irfg can be seen in Fig. . In addition, the response of
upf1 and irfg to the recent minor geomagnetic storms (detected by 3 h
ap and 1 h Dst indices) is apparent and also similar to the
post-processed IGS final combined GIM (igsg).
Data availability
The IGS real-time combined GIMs during the testing period are available from Zenodo at 10.5281/zenodo.5042622 in IONEX format . In addition, more archived IGS combined RT-GIMs can be found at http://chapman.upc.es/irtg/archive/, and the latest IGS combined RT-GIMs are available in real-time mode at http://chapman.upc.es/irtg/last_results/.
Conclusions
In this paper, we have summarized the computation methods of RT-GIMs from four
individual IGS ionosphere centers and introduced the new version of IGS
combined RT-GIM. According to the results of Jason-3 VTEC and dSTEC-GPS
assessment, it could be concluded as follows.
The real-time weighting technique for the generation of IGS combined RT-GIM performs well when it is compared with Jason-3 VTEC and dSTEC-GPS assessment.
The transition of UPC RT-GIM from USRG to UADG is obvious in all involved assessments and also demonstrates the sensibility of the real-time weighting technique to RT-GIMs when the accuracy of RT-GIMs is increased.
The quality of most IGS RT-GIMs is close to post-processed GIMs.
The difference among RT-GIMs with 20 min and full temporal resolution can be neglected over oceans in the Jason-3 VTEC assessment (see Fig. and Table ), while the difference is visible in some RT-GIMs over continental regions in the dSTEC-GPS assessment (see Table ). The lower accuracy of GIMs with full temporal resolution (2 or 5 min) might be related to the uneven distribution of ionospheric observations, the weight between predicted GIMs and real-time observations. Combined with the previous study , it is suggested to find a more suitable temporal resolution for the generation of RT-GIM in a sun-fixed reference frame.
In addition, the GEC evolution of UPC RT-GIM and IGS combined RT-GIM is close
to the GEC evolution of IGS final combined GIM in post-processing mode and
has an obvious response to the geomagnetic storm during the low-solar-activity
period. Future improvements might include the following.
Broadcast real-time rms maps that can be useful for the positioning users.
Increase the accuracy of high-temporal-resolution RT-GIMs. In addition, higher maximum spherical harmonic degrees might be adopted to increase the accuracy and spatial resolution of RT-GIMs.
Coinciding with a much larger number of RT-GNSS receivers in the future, the dSTEC weighting might be improved by replacing the “internal” with the “external” receivers, i.e., not used by any real-time analysis centers. In this way the weighting would be sensitive as well to the interpolation–extrapolation error of the different real-time ionospheric GIMs to be combined. And the resulting combination might behave better.
Increase the number of worldwide GNSS receivers used for the RT-dSTEC up to more than 100. In this way we will be able to study the potential upgrade of the present global weighting to a regional weighting among other potential improvements in the combination strategy.
Author contributions
QL wrote the manuscript. QL developed the updated combination software with contributions from DRD, HY and MHP. QL and MHP designed the research, with contributions from HY, EMM, DRD and AGR. QL, HY, EMM, MHP, ZL, NW, DL, AB, Q. Zhao and Q. Zhang provided the real-time GIMs of the corresponding IGS centers. AH, MS, GW and AS contributed in creating the framework of the real-time IGS service, the ionospheric message format and BNC open software updates. LA suggested the initial idea of this work. AK, StS, JF, AK, RGF and AGR contributed in the generation of rapid and final IGS GIMs used as additional references in the manuscript.
Competing interests
The contact author has declared that neither they nor their co-authors have any competing interests.
Disclaimer
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Acknowledgements
The authors are thankful to the collaborative and friendly framework of the International GNSS Service, an organization providing first-class open data and open products . The VTEC data from the Jason-3 altimeter were gathered from the NASA EOSDIS Physical Oceanography Distributed Active Archive Center (PO.DAAC) at the Jet Propulsion Laboratory, Pasadena, CA (10.5067/GHGMR-4FJ01), and the National Oceanic and Atmospheric Administration (NOAA). We are also thankful to GeoForschungsZentrum (GFZ) and to World Data Center (WDC) for Geomagnetism, Kyoto, for providing the ap and Dst indices.
Financial support
This research has been supported by the China Scholarship Council (CSC). The contribution from UPC-IonSAT authors was partially supported by the European Union-funded project PITHIA-NRF (grant no. 101007599) and by the ESSP/ICAO-funded project TEC4SpaW. The work of Andrzej Krankowski is supported by the National Centre for Research and Development, Poland, through grant ARTEMIS (grant nos. DWM/PL-CHN/97/2019 and WPC1/ARTEMIS/2019).
Review statement
This paper was edited by Christian Voigt and reviewed by two anonymous referees.
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