Ionospheric data assimilation is a powerful approach to reconstruct the 3-D distribution of the ionospheric electron density from various types of observations. We present a data assimilation model for the ionosphere, based on the Gauss–Markov Kalman filter with the International Reference Ionosphere (IRI) as the background model, to assimilate two different types of slant total electron content (TEC) observations from ground-based GPS and space-based FORMOSAT-3/COSMIC (F3/C) radio occultation. Covariance models for the background model error and observational error play important roles in data assimilation. The objective of this study is to investigate impacts of stationary (location-independent) and non-stationary (location-dependent) classes of the background model error covariance on the quality of assimilation analyses. Location-dependent correlations are modeled using empirical orthogonal functions computed from an ensemble of the IRI outputs, while location-independent correlations are modeled using a Gaussian function. Observing system simulation experiments suggest that assimilation of slant TEC data facilitated by the location-dependent background model error covariance yields considerably higher quality assimilation analyses. Results from assimilation of real ground-based GPS and F3/C radio occultation observations over the continental United States are presented as TEC and electron density profiles. Validation with the Millstone Hill incoherent scatter radar data and comparison with the Abel inversion results are also presented. Our new ionospheric data assimilation model that employs the location-dependent background model error covariance outperforms the earlier assimilation model with the location-independent background model error covariance, and can reconstruct the 3-D ionospheric electron density distribution satisfactorily from both ground- and space-based GPS observations.
The ionosphere is becoming more relevant to human society, with its reliance on modern technology, since the accuracy of navigation and quality of telecommunication is influenced by ionospheric conditions. Disruption of communications and navigation systems can have severe societal consequences. Even though the ionospheric observational techniques and the ionospheric models have gone through considerable development sustained over many decades, accurate monitoring and forecasting of the ionosphere conditions still presents obstinate challenges. Data assimilation procedures have recently come to play an important role in ionospheric research to overcome limitations of observations and models, and is an active area of research and development.
Some of the most comprehensive operational physics-based ionospheric data
assimilation systems have been developed by Utah State University (e.g.,
Schunk et al., 2005; Scherliess et al., 2006) and the University of Southern
California and Jet Propulsion Laboratory (e.g., Wang et al., 2004; Pi et al.,
2009; Komjathy et al., 2010). Lee et al. (2012) recently assimilated the
retrieved FORMOSAT-3/COSMIC (F3/C) electron density profiles into a general
circulation model of the thermosphere and ionosphere. Extensive variational
data assimilation procedures have been developed with an empirical
ionospheric model (e.g., Bust et al., 2004, 2007). Nicolls et al. (2009)
applied this methodology to improve the
The NOAA United States Total Electron Content (US-TEC) model (Fuller-Rowell
et al., 2006) is designed to specify TEC over the continental United States
(CONUS) from ground-based GPS slant TEC data. US-TEC uses the empirical
ionosphere model, International Reference Ionosphere 95 (IRI95) (Bilitza,
1997), as a background model, and uses the empirical orthogonal functions
(EOFs) and their coefficients (Spencer et al., 2004) to represent states in
the Kalman filter (Kalman, 1960; Kalman and Bucy, 1961). The average rms
(root mean square) error of US-TEC is 2.4 TEC units (Araujo-Pradere et al.,
2007). The Kalman filter is one of the most commonly used approaches to
ionospheric data assimilation. The Kalman filter update equation is given as
Mariner 4 first applied the RO observation technique to observe the Mars atmosphere and ionosphere in 1965 (Kliore et al., 1965). MicroLab-1 GPS/MET was launched in 1995 and applied to monitor the Earth's atmosphere and ionosphere by using the GPS RO technique (Hajj and Romans, 1998; Kursinski et al., 1997). The integrated content of ionospheric electron density, namely total electron content (TEC), has been measured between the GPS satellites and MicroLab-1. This is a way to observe the ionosphere horizontally at different altitudes and obtain the electron density profile using the Abel inversion technique. The F3/C mission was launched in April 2006, and has six micro-satellites in the different orbital planes. The GPS radio occultation experiment (GOX) is one of the satellite mission objectives, and observes the ionosphere and atmosphere vertical structure by using the RO observation technique. RO observations, particularly from F3/C, have significantly improved our capability of monitoring the global ionosphere (Cheng et al., 2006; Schreiner et al., 2007).
The overarching goal of our study is to assimilate not only the ground-based
GPS slant TEC data but also F3/C RO slant TEC data into US-TEC. However, the
original scheme was designed for assimilation of slant TEC between
ground-based stations and GPS satellites, and is not ideal for assimilation
of the RO slant TEC data. New data assimilation approaches that can better
accommodate the RO data need to be developed. To this end, our study attempts
to make the scheme more flexible; thus the Kalman filter equations will now
be solved with respect to the grid-point electron density values (i.e.,
We use observing simulation system experiments (OSSEs), designed to mimic
realistic observing systems of the ground-based GPS, and F3/C RO data to
assess the impact of different types of the background model error covariance
and the quality of assimilation analyses. Assimilation results are further
validated with Millstone Hill incoherent scatter radar (ISR) electron density
data, and compared with the F3/C GOX electron density profiles retrieved by
the Abel inversion technique. Assimilation analyses are also presented in the
form of TEC maps during both the daytime and nighttime. The use of F3/C RO
data in data assimilation procedures is shown to improve both the vertical
and horizontal structure of the ionospheric electron density distribution.
The model domain extends from
When ground-based GPS and F3/C RO observation data are ingested into the data
assimilation model, the observational errors need to be taken into account.
Data from 200 ground-based GPS stations on the CONUS and F3/C RO slant TEC
are used in examples shown later. More than 2000 GPS stations exist on the
ground all over the world, and can yield the high-resolution TEC observations
to determine horizontal structures of the ionosphere for monitoring various
ionospheric phenomena and diurnal variations (Liu et al., 1996). However,
most stations do not provide the differential code bias (DCB) of GPS
receivers. Kakinami et al. (2009) used the Global Ionospheric Map (GIM)
developed by the Jet Propulsion Laboratory (Mannucci et al., 1998) as a reference
to eliminate the instrumental biases. The differential instrumental biases of
GPS receivers are estimated by the GIM minimum TEC value during 04:00 and
06:00 local time at GPS receivers, while the DCB of GPS satellite is
calibrated by using the Center for Orbit Determination in Europe (CODE)
values (Schaer, 1999). The ground-based GPS slant TEC in this study is
treated as DCB-free TEC after these DCB calibration processes. For
space-based RO, the main error sources of the absolute TEC value obtained
from RO include multipath effects, DCBs from GPS and low Earth orbit (LEO)
satellites, and errors in leveling of the phase to the pseudorange TEC (Yue
et al., 2011b). This study uses the F3/C podTec data produced by the COSMIC
Data Analysis and Archival Center (CDAAC), and assumes that the absolute TEC
values are free of DCB and multipath errors because these major errors are
eliminated by CDAAC. In ground-based GPS observations with elevation angles
of 20
Every GPS satellite can transmit signals at dual-frequency carrier phases
(L1: 1575.42 MHz; L2: 1227.60 MHz). Coarse/acquisition (C/A: 1.023 MHz)
and precision codes (P1: 10.23 MHz) are coded on the L1 carrier phase, and
another precision code (P2: 10.23 MHz) is coded on the L2 carrier phase. The
absolute and relative TEC can be calculated from the pseudorange and carrier
phase, respectively (Sardón et al., 1994; Liu et al., 1996). Since the
satellite and ground-based receivers error sources influence the precision of
TEC calculated from pseudorange (TEC
Data thinning is required because sampling space and time frequency of the
GPS technique is significantly higher than the temporal and spatial
resolution of data assimilation analysis. In this study, the grid-point
resolution is 2
The main sources of GPS data errors have been described in above. Errors resulting from the DCB of GPS satellites, F3/C satellites, and ground-based GPS stations have been reduced before ingestion through the various calibration processes mentioned above. The leveling TEC error and representativeness error are the two types of errors that are combined to model the observation error covariance.
We develop two types of the background model error covariance in this study
(
Here, the location-dependent correlation is designed by separating it into
two parts: the vertical correlation and the horizontal correlation, and by
using the EOFs to represent these correlations. First, we compute EOFs from
the 62 different IRI ionospheric electron density distributions,
Figure 1a shows the vertical EOFs at a given longitude and latitude location. The location-independent vertical correlation (Fig. 1b) illustrates that the correlation is identical at every altitude, as calculated by using the same Gaussian function, while the location-dependent vertical correlation (Fig. 1c) shows that the vertical correlation is different at different altitudes. The vertical correlation at low altitude (below 150 km) is higher with lower-altitude locations but lower with higher-altitude locations. The vertical correlation at high altitude (above 150 km) is, on the other hand, higher with higher-altitude locations but lower with lower altitudes. This result suggests that the vertical correlation is strongly dependent on altitude locations. Since the vertical correlation is determined from the IRI empirical model outputs, rather than real observations, the vertical correlation used here is not free of errors when assimilating the real data. The length scale of localization function for altitude changes at different altitudes to reflect the vertical correlation length scale, which varies considerably with altitude.
The vertical correlation at long
The horizontal correlation at 00:00 UTC.
The idea of calculating the horizontal correlation, the second part of location-dependent
correlation, is similar to the vertical correlation. The
The horizontal correlation is obtained after normalization and localization
as in Eq. (8); this step is the same as calculating the vertical correlation.
The OSSEs, in which synthetically generated observations sampled from the IRI model output (i.e., the simulation truth) are assimilated, provide the assessment of the data assimilation (DA) procedure under idealistic conditions. A total of six different OSSEs have been conducted to examine the effects of different types of background model error covariance on the assimilation analysis quality. The simulation results are shown for the North American continent at 00:00 UTC on 5 February 2008 (Fig. 3). Note that the simulation truth and the background model states are different in the OSSEs presented here. The simulation truth is calculated from IRI with the lower IG index rather than the real IG index. This parameter setting makes synthetically generated observations of electron density lower than the climatological prediction by IRI in an effort to account for the tendency of IRI to overestimate the TEC during the extreme solar minimum conditions. This makes the simulation truth different from the background state. Two different kinds of slant TEC data are considered in the OSSEs: ground-based GPS data and F3/C occultation data.
The OSSE result of the data assimilation model for 00:00 UTC on
5 February 2008.
Figure 3a displays the distributions of observations used in these
experiments: ground-based GPS station (black point) and F3/C RO slant TEC
path (red line). Six different experiment settings are as follows:
(1) location-independent background model error covariance with synthetic
ground-based GPS data (Fig. 3b), (2) location-independent background model
error covariance with synthetic F3/C RO data (Fig. 3c),
(3) location-independent background model error covariance with both
ground-based and F3/C RO data (Fig. 3d), (4) location-dependent background
model error covariance with synthetic ground-based GPS data (Fig. 3b),
(5) location-dependent background model error covariance with synthetic
F3/C RO data (Fig. 3c), and (6) location-dependent background model error
covariance with both ground-based and F3/C RO data (Fig. 3d). The OSSE
results are shown at long
The DA and background model IRI TEC map of the North American Continent at daytime (14:00 to 17:00 UTC, top three rows) and 18:00 to 21:00 UTC (bottom three rows). Each time period has three different TEC maps, including a DA TEC map using ground-based GPS data, an IRI TEC map, and a DA TEC map using ground-based GPS and F3/C RO data.
The DA and background model IRI TEC map of the North American Continent at nighttime (02:00 to 05:00 UTC, top three rows) and 06:00 to 09:00 UTC (bottom three rows). Each time period has three different TEC maps, including a DA TEC map using ground-based GPS data, an IRI TEC map, and a DA TEC map using ground-based GPS and F3/C RO data.
We have conducted several data assimilation experiments over the CONUS with real ground-based GPS and F3/C RO slant TEC data on 21 October 2008. Assimilation results are presented as TEC, which is the column-integrated electron density from 80 to 1000 km. Results are compared to the background model TEC to examine the impact of F3/C RO data as well as ground-based GPS data. Figures 4 and 5 show TEC maps for the daytime (14:00–21:00 UTC) and nighttime (02:00–09:00 UTC) on 21 October 2008. At each hour UTC, three TEC maps are shown: a DA TEC map using ground-based GPS data, an IRI background TEC map, and a DA TEC map using both ground-based GPS and F3/C RO data. It is clear that both types of data can modify the climatological TEC distribution predicted by the IRI successfully. Through comparison of two DA TEC maps, the influence of F3/C RO data is evident, particularly over the ocean, where ground-based GPS stations are absent. For instance, see the TEC maps at 02:00 UTC in Fig. 5, in which TEC have been updated over the ocean thanks to F3/C RO data. Our data assimilation system can effectively assimilate both space-based and ground-based GPS observations in the daytime and nighttime.
The use of the location-dependent background model error covariance in the
data assimilation scheme is essential when assimilating both ground-based GPS
and F3/C RO data as suggested by the OSSE experiments. The accuracy of the
data assimilation model must now be validated in terms of the model's ability to
assimilate the real observation data. Here, the Millstone Hill incoherent
scatter radar data are used to validate electron density profiles obtained
from the assimilation of real ground-based GPS and F3/C RO data. Figure 6
displays the profiles at each 15 min interval between 16:00 and 17:45 UTC
on 21 October 2008. Shown are the background model IRI (black), the data
assimilation result (red is the DA electron density located at Millstone
Hill; the green line is the DA electron density assimilating only ground-based
GPS data), and the Millstone Hill data and related error bar (blue). The data
assimilation results are obtained every 15 min. The displayed incoherent
scatter radar profile is the median value over 15 min. There are three
F3/C RO observation events over the region during this period. The altitude
grids where F3/C RO paths intersect with the ISR line of sight are indicated
by green boxes at 16:15, 16:45, and 17:45 UTC. The F3/C RO paths pass
through at different altitude regions over Millstone Hill over this period;
they pass through the
Comparison of data assimilation results and Millstone Hill incoherent scatter radar observations from 16:00 to 17:45 UTC, with a time period of 15 min. The red line is the DA electron density located at Millstone Hill and the green line is the DA electron density assimilating only ground-based GPS data, while the black line is the background of the DA model. The blue line is the observation and error bars of Millstone Hill incoherent scatter radar. The green boxes indicate that the altitude had F3/C RO passing through.
The comparison of the data assimilation results, Millstone Hill
incoherent scatter radar observation, and F3/C electron density profile from
the Abel inversion.
The F3/C electron density profile calculated from the Abel inversion
(obtained from CDAAC) can also be compared to our data assimilation analysis.
The comparison is presented for 16:15 UTC on 21 October 2008, when the RO
path is located close to Millstone Hill. Figure 7a displays the 3-D
observing geometry of Millstone Hill ISR (blue) and F3/C RO (red), and the
TEC map from the DA result is shown on the longitude–latitude plane at the
bottom. Since the ISR location and F3/C RO tangent point location are
different, we validated our DA result with ISR and F3/C RO electron density
separately. Figure 7b compares vertical electron density profiles from the
ISR and data assimilation analysis at the Millstone Hill location. The ISR
error bar plotted along the ISR profile suggests high measurement
uncertainty in the upper portion of the profile. The data assimilation
electron density profile agrees well with ISR from altitude 200 to 400 km,
where the ISR error is relatively small, including
In this study, we develop a new background model error covariance model to account for spatially variable correlation patterns of the model errors. Even though the location-dependent covariance model reflects more realistic correlations, the OSSE results indicate that both location-independent and location-dependent covariance work equally well for assimilation of ground-based GPS data. (See Fig. 3b, where electron density profiles obtained by using both types of the covariance models are shown to produce similar results and compare well with the simulation truth.) This result suggests that the vertical and horizontal error correlation might not have significant importance when assimilating the ground-based GPS slant TEC. Since the radio signal is transmitted from GPS satellites to ground-based receivers, the ground-based GPS slant TEC data tend to contain more information about the horizontal ionospheric structure and less about the vertical ionospheric structure. Vertical correlation in the background model error covariance is rather irrelevant in inverting the ground-based GPS slant TEC data since they are a nearly vertically integrated quantity. Moreover, the horizontal extent of ground-based GPS observations is mostly limited in the vicinity of ground-based stations, and therefore the long-range horizontal correlation does not play a significant role either.
RO slant TEC values are computed from radio signals transmitted from GPS satellites to LEO satellites that pass through the ionosphere at different altitudes over extensively large horizontal areas, and F3/C RO data can thus provide vertically resolved ionospheric information. To invert RO slant TEC data accurately, the vertical and horizontal correlation in the background model error covariance needs to be realistic. The OSSE results presented in Fig. 3c demonstrate this point, showing that electron density profiles obtained using a more realistic covariance model are closer to the simulation truth. When assimilating the F3/C RO data, it is therefore important that the background model error covariance reflects realistic location-dependent correlation structures.
The accuracy of the background model error covariance affects the quality of data assimilation analyses, especially when assimilating different kinds of GPS data. The OSSE results shown in Fig. 3d, obtained from assimilation of ground-based and RO synthetic data, illustrate this point clearly. Electron density profiles estimated by using the location-dependent error covariance are closer to the simulation truth in comparison to the cases with the location-independent error covariance. Even though the OSSE electron density profiles obtained by using the location-independent error covariance is reasonable for assimilating ground-based GPS data alone, the results are deteriorated when assimilating the same data in addition to the RO data. These detailed comparisons suggest that the choice of the background model error covariance needs to be suitable for all types of GPS data being assimilated; otherwise the accuracy of data assimilation analysis would not be optimal.
It should be noted that the current study has not considered the Kalman filter forecast step, so our approach is closer to the optimal interpolation for the moment. In the Kalman filter, the background model error covariance is expected to evolve and become more realistic over time through a recursive application of update and forecast steps in theory. In reality, it is difficult to fully incorporate nonlinear ionospheric dynamics into the Kalman filter forecast step. The model dynamics are often simplified, and the evolution of background (forecast) model error covariance is therefore approximated. The current study represents a low-dimensional modeling of the background model error covariance, which can facilitate the future implementation of the Kalman filter in the global domain. This point will be demonstrated in our future work. As part of our future work, the Taiwan Ionospheric Model (TWIM), which is constructed from F3/C RO electron density profiles (Tsai et al., 2009), can be used in the place of the IRI model in our data assimilation study to increase the accuracy of background model vertical structure.
To validate the electron density profiles, the DA results are evaluated and
compared to the Millstone Hill ISR data from 16:00 to 17:45 UTC at every
15 min interval on 21 October 2008. Both ground-based GPS and
F3/C observations are located closed to the ISR at three intervals: 16:15,
16:45, and 17:45 UTC. In these three time periods, the rms deviation between
ISR data and DA results obtained from assimilation of RO and ground-based GPS
data is 4.06
The tangent points of the F3/C are aligned with the Millstone Hill ISR
line of sight at 16:15 UTC on 21 October 2008, when the DA results compare
well with the ISR electron density profile. The comparison of our DA results
with the ISR electron density profile and with the profile retrieved from the
F3/C using the Abel inversion is shown in Fig. 7b and c, respectively. This
comparison reflects the respective observing geometry of ISR and F3/C RO
techniques, since the later one is slightly veered from vertical. The DA
electron density profile agrees well with the ISR data from altitude 200 to
400 km, where the ISR error is relatively small, including
The ground-based GPS technique can provide valuable continual monitoring of the ionosphere, but its spatial coverage is regional. To achieve global monitoring of the ionosphere, including the oceans and remote regions where it is difficult to deploy ground-based stations, space-based observing techniques like the F3/C are crucial. TEC maps, shown in Figs. 4 and 5 for both daytime and nighttime, demonstrate this point. Because of its spatially limited observing geometry, the ground-based GPS observation can modify the background ionosphere horizontal structure only in the vicinity of station locations. On the other hand, the space-based GPS technique can provide greater spatial coverage because RO paths pass through the ionosphere rather horizontally. Data assimilation approaches, such as the one presented here, can take advantage of both observing techniques to improve the global ionospheric specification.
In addition, the TEC maps display the feature akin to the plasmaspheric tail (ionospheric plume) at 20:00 UTC (Fig. 4) (Foster et al., 2002). The similar plasmaspheric tail signature is shown in both assimilation results but is not seen in the background model. Our data assimilation procedure has the capability to reconstruct realistic transient ionospheric features, such as plasmaspheric tails, that are absent in IRI. Resulting assimilation analyses can be used for storm time studies to identify the plasmaspheric foot points in the ionosphere.
In this study, we presented a new approach to assimilate F3/C RO data as well as ground-based GPS data into the background model IRI and examined the impact of RO data on the reconstructed 3-D ionospheric election density structure. Unlike the current US-TEC model, which solves Kalman filter equations with respect to EOF coefficients, we developed a new data assimilation procedure in which the Kalman filter equations are solved in terms of grid-point electron density in order to accommodate a more flexible regularization strategy. Four main conclusions were drawn from our results.
The first conclusion is, as illustrated by the OSSE experiment results, that the location-dependent model error covariance facilitated inverting both ground-based GPS and F3/C RO slant TEC data independently, and that it is a key to successfully assimilating both data at the same time. This conclusion was drawn from demonstrating the limitation of the location-independent covariance model (based on the Gaussian function) for the assimilation of RO observational data, and developing a new covariance model whose correlation structures depend on longitude, latitude, and altitude location. The location-dependent covariance model was constructed by representing vertical and horizontal correlations with EOFs and their coefficients as shown in Figs. 1 and 2. OSSE experiments with the location-independent model error covariance showed that results were satisfactory for ground-based GPS data assimilation, but the OSSE result assimilating F3/C RO slant TEC does not agree well with the simulation truth. Therefore, the OSSE result illustrated that the location-dependent model error covariance worked well with both datasets separately, and even better assimilating both simultaneously.
Second, we validated assimilation analyses using Millstone Hill ISR data and concluded that assimilation of ground-based and RO data using our new procedure improved the agreement with ISR electron density profiles. This was true particularly when F3/C RO data are present in the vicinity of Millstone Hill, since the DA scheme is able to correct altitude structures quite well.
The third conclusion is that our scheme can produce a more robust profile than the Abel inversion thanks to regularization through the use of more realistic background model error covariance in the Kalman filter update equation. This point was demonstrated by sampling our DA results along the RO tangent points, and comparing them with F3/C RO electron density profiles calculated from the Abel inversion, as shown in Fig. 7 for the Millstone Hill location. Our DA results are generally similar to the Abel inversion results, but, importantly, our scheme was able to produce more robust profiles due to an improved regularization in inversion methods.
Our final conclusion is that the F3/C RO could improve the electron density results over greater areas, including oceans and remote regions where no ground-based stations exist. Furthermore, the F3/C RO data have the potential to improve the altitude structures of DA analysis. For the F3/C mission, 1000–2500 RO events per day (3000 at maximum) have occurred; however the current RO global coverage is not complete at a given time. This should be greatly improved when FORMOSAT-7/COSMIC-2 (F7/C2), with 12 micro-satellites, is launched in 2016 and 2018. Each micro-satellite will be equipped with the appropriate satellite signal receiver to conduct the RO experiment with GNSS and GLONASS. This new mission is expected to yield more than 14 000 RO events per day. By assimilating F7/C2 RO data into our data assimilation model, the global ionosphere specification will be significantly improved. Our new DA procedure can also be incorporated into the NOAA/SWPC ionospheric assimilation model US-TEC to increase the assimilation analysis accuracy. With the expanded availability of RO data, the electron density distribution analysis will be improved over greater regions, including areas where ground-based GPS stations are absent, and the approach presented in this paper supports such future prospects.
Chi-Yen Lin sincerely thanks Karen Fay O'Loughlin for her helpful assistance with the paper. Support for this study is provided through NASA award NNX09AJ83G to the University of Colorado at Boulder, and the Taiwan National Science Council (NSC) grant NSC 102-2628-M-008-001. The authors gratefully acknowledge the International GNSS Service (IGS) for providing GPS data and COSMIC Data Analysis and Archival Center (CDAAC) and the Taiwan Analysis Center for COSMIC (TACC) for the FORMOSAT-3/COSMIC data. Radar observations at Millstone Hill are supported by a cooperative agreement between the US National Science Foundation and the Massachusetts Institute of Technology. Edited by: U. Foelsche