Swarm SCARF Dedicated Ionospheric Field Inversion chain
© The Society of Geomagnetism and Earth, Planetary and Space Sciences (SGEPSS); The Seismological Society of Japan; The Volcanological Society of Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences; TERRAPUB. 2013
Received: 2 April 2013
Accepted: 26 August 2013
Published: 22 November 2013
The geomagnetic daily variation at mid-to-low latitudes, referred to as the geomagnetic Sq field, is generated by electrical currents within the conducting layers of the ionosphere on the dayside of the Earth. It is enhanced in a narrow equatorial band, due to the equatorial electrojet. The upcoming ESA Swarm satellite mission, to be launched end of 2013, will consist of three satellites in low-Earth orbit, providing a dense spatial and temporal coverage of the ionospheric Sq field. A Satellite Constellation Application and Research Facility (SCARF) has been set up by a consortium of research institutions, aiming at producing various level-2 data products during the Swarm mission. The Dedicated Ionospheric Field Inversion (DIFI) chain is a SCARF algorithm calculating global, spherical harmonic models of the Sq field at quiet times. It describes seasonal and solar cycle variations, separates primary and induced magnetic fields based upon advanced 3D-models of the mantle electrical conductivity, and relies on core, lithospheric and magnetospheric field models derived from other SCARF algorithms for removing non-ionospheric fields from the data. The DIFI chain was thoroughly tested on synthetic data during the SCARF preparation phase; it is now ready to be used for deriving models from real Swarm data.
A small fraction of the Earth’s magnetic field is generated by electrical currents within the conductive layers of the ionosphere, near 110 km altitude. On geomagnetically quiet days, at mid-to-low latitudes, the ionospheric magnetic field has an amplitude of 10 to 50 nT on the ground and is referred to as the “Sq” magnetic field (see, e.g., Richmond and Thayer, 2000). It undergoes a characteristic daily variation, visible in geomagnetic observatory recordings, where the Z component increases (in absolute value) from sunrise to noon and decreases from noon to sunset. In a ±5? latitudinal band centered on the geomagnetic dip-equator, the amplitude of this daily variation is even larger and can reach up to 100 nT on the ground around noon. The ionospheric field in this band is caused by the equatorial electrojet, a thin current flowing eastward along the geomagnetic dip-equator.
Global spherical harmonic models of the Sq field have classically been determined from observatory data, relying on the global observatory network. Such models (e.g., Schmucker, 1999a, b; Takeda, 2002) provide a description of the large-scale current system generating the Sq field, as well as its seasonal and solar cycle variability. Use of magnetic measurements from low-Earth orbiting satellites such as ϕrsted and CHAMP makes it possible to model the Sq field up to higher spherical harmonic degrees, and to also model the equatorial electrojet field (Sabaka et al., 2002, 2004). However, satellite data are collected above the ionosphere. They cannot separate the primary ionospheric field from the secondary, induced field generated by electrical currents within Earth’s mantle. Such a separation is possible, however, if a pre-determined mantle conductivity model is available.
The upcoming ESA Swarm satellite mission, to be launched in 2013, will provide measurements of the Earth’s magnetic field with unprecedented precision from three identical satellites orbiting at different altitudes and local times (Friis-Christensen et al., 2006). Several research institutions have teamed up with ESA to form the Swarm Satellite Constellation Application and Research Facility (SCARF), a distributed processing facility that will produce geomagnetic field models during the Swarm mission (Olsen et al., 2013). Two of these models will be spherical harmonic descriptions of the ionospheric magnetic field at mid-to-low latitudes, i.e., below 55? dipole latitude. One of them will be calculated as part of a comprehensive inversion, where all major sources of the geomagnetic field will be calculated simultaneously (Sabaka et al., 2013); the other will be calculated through a dedicated inversion, after removing the magnetic fields generated by other sources from the data.
In the present paper, we introduce the Swarm Dedicated Ionospheric Field Inversion (DIFI) algorithm (Section 2), which will be used for calculating the dedicated ionospheric field from Swarm data. The DIFI chain takes into account the seasonal and solar cycle variability of the field. It was thoroughly tested during its development phase using synthetic data. Results of these tests are presented in Section 3. The DIFI chain is one of the three chains developed by IPGP within SCARF; other chains are the Dedicated Lithospheric Field Inversion (DLFI) chain (Thébault et al., 2013) and the Equatorial Electric Field (EEF) inversion chain (with NOAA, Alken et al., 2013).
2. DIFI Algorithm
2.1 Data pre-processing
During the exploitation phase, the DIFI algorithm will be used to calculate two types of models: ionospheric field models calculated over at least one year of data, which will include a description of the seasonal variation of model coefficients, and ionospheric field models calculated over less than one year of data (typically three to six months), with coefficients assumed constant with respect to season. The second type of model will be calculated only during the first year of the mission, to provide a first model within a few months after the commissioning phase. In what follows, we describe the algorithm to be used for the calculation of a full model, including seasonal variation, assuming one full year of level 1b magnetic data is available as input.
By default, the DIFI algorithm reads all level 1b vector magnetic data from Swarm A, one of the two satellites orbiting side-by-side at about 460 km altitude, and from Swarm C, the satellite orbiting at a higher altitude of about 530 km, in a different local time sector. Several failure cases have been investigated as part of the preparation phase within SCARF, for example the complete failure of one satellite or the lack of vector data from one of the satellites. If such an unhappy event were to occur, the DIFI algorithm would still be able to ingest reduced level 1b dataset. In what follows, we describe the nominal scenario where level 1b vector magnetic data are available from both Swarm A and C satellites.
The next step of the pre-processing block is data correction. It aims at removing non-ionospheric contributions from the total vector field recorded by each satellite. Three main sources are considered: the core, the lithosphere and the electrical currents in the magnetosphere. By default, SCARF dedicated (Hamilton, 2013; Rother et al., 2013; Thébault et al., 2013) and/or comprehensive (Sabaka et al., 2013) models are used to remove contributions from these sources. If needed, non-SCARF, auxiliary models will be considered during the exploitation phase to improve the quality of the final model.
Observatory data (hourly mean values, see Macmillan and Olsen, 2013) can also be used by the DIFI algorithm, although not in the default mode. These data are pre-processed in a similar way: first, they are selected according to geomagnetic Kp and Dst indices, as well as IMF By and Bz components; second, they are corrected for the core, lithospheric and magnetospherie fields using the same dedicated or comprehensive SCARF models. Observatory biases, i.e., the small-scale lithospheric field not described by these models, are left as variables to be determined by the inversion.
2.2 Model parameterization
The DIFI algorithm relies on the same ionospheric field model parameterization as the comprehensive models (see, e.g., Sabaka et al., 2000, 2002, 2013). In what follows, we briefly summarize the main features of this parameterization, using similar matrix notations as Sabaka et al. (2000).
Primary sources of the ionospheric magnetic field at mid-to-low latitudes are electrical currents flowing in the E-region of the ionosphere, at about h = 110 km altitude. The time-varying magnetic field generated by these currents induces secondary currents in the upper layers of the Earth’s electrically conducting mantle, which in turn contribute to the total ionospheric magnetic field. The spherical harmonic modeling of the ionospheric magnetic field relies on the assumption that Swarm satellites fly above these ionospheric sources. As a consequence, the ionospheric magnetic field B (i.e., observations minus contributions from the core, lithosphere and magnetosphere) may be expressed as B = − ΔV, where V is a magnetic potential.
It is also assumed that the ionospheric magnetic field responds linearly to solar activity, parameterized by the solar radio flux index F10.7 (expressed in solar flux units, or SFU, where 1 SFU = 10−22 W m−2 Hz−1). Then is replaced by , where the so-called Wolf ratio N = 14.85 × 10−3 SFU−1 was determined by Olsen et al. (1993). It is worth noting that the Wolf ratio actually varies with season (see, e.g., Penquerc’h and Chulliat, 2009). This effect will be investigated during the Swarm mission and could lead us to develop a more sophisticated parameterization of the response to solar activity in later DIFI models.
The quasi-dipole vector of coefficients in (21)–(22) is truncated for 1 ≤ k ≤ Kmax,− min(k, Lmax ) ≤ l ≤ min(k, Lmax ), s min ≤ s ≤ s max and p min ≤ p ≤ p max . The dipole vector of coefficients ϵ in (9)–(10) (as well as (18)) is truncated for 1 ≤ n ≤ Nmax, − min(n, Mmax ) ≤ m ≤ min(n, Mmax ), s min ≤ s ≤ s max and p min ≤ p ≤ p max . This leads to a total of N q = Lmax ( Lmax + 2) + (Kmax − Lmax )(2 Lmax + 1) quasi-dipole coefficients and dipole coefficients for each pair of wavenumbers (p, s). In the tests reported in Section 3, the ionospheric field was modelled in quasi-dipole coordinates up to degree Kmax = 45 and order Lmax = 5 (hence N q = 475 coefficients), with diurnal variations from p min = 0 to pmax = 4 (i.e., down to a period of 6 hours) and seasonal variations from s min = −2 to s max = 2 (i.e., constant, annual and semi-annual variation). These parameters are the ones set in the original SCARF specifications (Swarm Level 2 Processing System Consortium, 2013). Note that p is arbitrarily taken positive, so that modes propagate westward for l > 0 (or m > 0) and eastward for l ≤ 0 (or m ≤ 0). Unlike Sabaka et al. (2000, 2002), we do not select only modes closest to the local time modes l = p. A numerical investigation of Eq. (13) shows that Nmax = 60 and Mmax = 12 (hence N d = 1368 coefficients) are sufficient to achieve convergence of the D matrix. The modulus of the obtained matrix is shown in Fig. 2.
The scalar potential V2 of the secondary (induced) ionospheric field is expressed as in Eq. (25), but with real coefficients ; these are obtained by taking the real part of the product ι H S i in Eqs. (4)–(5).
3. Test Results
During the preparation phase, the DIFI algorithm was tested using synthetic data. The way the synthetic orbits and magnetic data were generated is described in Olsen et al. (2013). We used only one year of synthetic data, from January 1, 2000 to December 31, 2000, and relied on real Kp,Dst, IMF and F10.7 values for the selected period.
The synthetic data were selected using the following criteria: K p ≤ 2 o , −20 nT ≤ Dst ≤ 20 nT, −8 nT ≤+ IMF B y ≤ 8 nT and −2 nT ≤ IMF B z ≤ 6 nT. Starting from synthetic Level 1b 1 Hz data, the selection process lead to 583705 data triples for each satellite A and C. The data were further decimated so that the time difference between two successive data never fell below 15 s, which corresponds to a minimum distance of about 105 km (since Swarm satellites orbit at about 7 km/s).
Removal of non-ionospheric contributions were implemented in different ways, depending on the tests carried out. During the so-called “AR1 test”, data were corrected using the same reference field models as the ones used for generating the synthetic data (see Olsen et al., 2013, for details about these models). As the random noise added to the synthetic data had a very small standard deviation (between 0.1 and 0.7 nT, depending on the component) compared to the typical amplitude of ionospheric fields, the data after correction were very close to the synthetic ionospheric field data themselves. Thus, the AR1 test essentially amounted to a closed-loop simulation of both the pre-processing and inversion blocks. During the second, so-called “AR2 test”, data were corrected using core, lithospheric and magneto-spheric field models derived as part of the test by SCARF partners, thus imperfectly reproducing the contribution of each source to the synthetic data, as would be the case with real data.
For both tests, we used the same Q matrix as the one used for generating the synthetic dataset (see Olsen et al., 2013, for details). This matrix was derived from a 3D electrical conductivity model of the mantle, including oceans, designed by Kuvshinov et al. (2006). We used the D matrix already mentioned in Section 2.2 and presented in Fig. 2.
3.1 AR1 test
Residual statistics (in nT) for AR1 and AR2 tests.
0.00 ± 0.15
0.01 ± 1.77
0.00 ± 0.11
0.00 ± 2.88
−0.01 ± 0.11
0.00 ± 2.37
ǀ90 − ¸ d ǀ ≤ 55°
0.00 ± 0.15
0.01 ± 1.78
0.00 ± 0.10
−0.01 ± 2.75
−0.01 ± 0.10
0.00 ± 2.04
Model performances (as defined in the main text) for AR1 and AR2 tests.
3.2 AR2 test
4. Concluding Remarks
In the present paper, we described the algorithm of the DIFI chain to be used during the upcoming Swarm mission to calculate global, spherical harmonic models of the quiet-time ionospheric field at mid-to-low latitudes. This algorithm relies on quasi-dipole coordinates to minimize the number of parameters, while describing the smallest spatial features of the average field such as the equatorial electro-jet. It can take advantage of a 3D conductivity model of the mantle and oceans when separating the primary and induced fields.
Closed-loop tests using synthetic data showed that the DIFI algorithm is able to reproduce the original primary and induced ionospheric fields to a very high accuracy, at ground and satellite altitudes. Tests relying on other SCARF models produced from the same dataset for data correction of the core, lithospheric and magnetospheric fields revealed that the pre-processing block of the algorithm is very sensitive to the quality of the correcting models. This problem is specific to the DIFI chain, as this chain is the last in the sequence of dedicated inversion chains to be processed. As a result, all errors made by previous chains in the sequence cascade down to the DIFI input. However, the inversion block proved remarkably stable with respect to these input errors; it is possible to calculate a meaningful ionospheric field, with performances within the threshold requirement, even when starting from imperfectly corrected data. During the exploitation phase, no reference field will be available to validate the DIFI chain output. The validation will be made by comparing the total field at ground with measurements from geomagnetic observatories.
The research reported here was financially supported by the Centre National d’Etudes Spatiales (CNES) through the “Travaux préparatoires et exploitation de la mission Swarm” project, and by the European Space Agency (ESA) through ESTEC contract 4000102140/10/NL/JA “Development of the Swarm Level 2 Algorithms and Associated Level 2 Processing Facility”. The authors thank the reviewers for their very helpful comments. This is IPGP contribution number 3423.
- Alken, P., S. Maus, P. Vigneron, O. Sirol, and G. Hulot, Swarm SCARF equatorial electric field inversion chain, Earth Planets Space, 65, this issue, 1309–1317, 2013.View ArticleGoogle Scholar
- Emmert, J. T., A. D. Richmond, and D. P. Drob, A computationally compact representation of Magnetic-Apex and Quasi-Dipole coordinates with smooth base vectors, J. Geophys. Res., 115(A8), 1–13, doi:10.1029/2010JA015326, 2010.Google Scholar
- Friis-Christensen, E., H. Lühr, and G. Hulot, Swarm: A constellation to study the Earth’s magnetic field, Earth Planets Space, 58, 351—358, 2006.View ArticleGoogle Scholar
- Kuvshinov, A., T. Sabaka, and N. Olsen, 3-D electromagnetic induction studies using the Swarm constellation: Mapping conductivity anomalies in the Earth’s mantle, Earth Planets Space, 58, 417—427, 2006.View ArticleGoogle Scholar
- Hamilton, B., Rapid modelling of the large-scale magnetospheric field from Swarm satellite data, Earth Planets Space, 65, this issue, 1295–1308, 2013.View ArticleGoogle Scholar
- Macmillan, S. and N. Olsen, Observatory data and the Swarm mission, Earth Planets Space, 65, this issue, 1355–1362, 2013.View ArticleGoogle Scholar
- Olsen, N., The solar cycle variability of lunar and solar daily geomagnetic variations, Ann. Geophys., 11, 254–262, 1993.Google Scholar
- Olsen, N., E. Friis-Christensen, R. Floberghagen, P. Alken, C. D Beggan, A. Chulliat, E. Doornbos, J. T. da Encarnaşão, B. Hamilton, G. Hulot, J. van den IJssel, A. Kuvshinov, V. Lesur, H. Lühr, S. Macmillan, S. Maus, M. Noja, P. E. H. Olsen, J. Park, G. Plank, C. Püthe, J. Rauberg, P. Ritter, M. Rother, T. J. Sabaka, R. Schachtschneider, O. Sirol, C. Stolle, E. Thébault, A. W. P. Thomson, L. Tϕffner-Clausen, J. Veí158, Column 20:imský, P. Vi-gneron, and P. N. Visser, The Swarm Satellite Constellation Application and Research Facility (SCARF) and Swarm data products, Earth Planets Space, 65, this issue, 1189–1200, 2013.View ArticleGoogle Scholar
- Penquerc’h, V. and A. Chulliat, Variability of the Sq magnetic field with the solar radiation flux F10.7, in Proceedings of ESA s Second Swarm International Science Meeting, 2009.Google Scholar
- Richmond, A. D., Ionospheric electrodynamics using magnetic apex coordinates,J. Geomag. Geoelectr, 47, 191–212, doi:10.5636/jgg.47.191, 1995.View ArticleGoogle Scholar
- Richmond, A. D. and J. P. Thayer, Ionospheric electrodynamics: A tutorial, in Magnetospheric Current Systems, Geophysical Monograph 118, American Geophysical Union, 131–146, 2000.Google Scholar
- Rother, M., V. Lesur, and R. Schachtschneider, An algorithm for deriving core magnetic field models from the Swarm data set, Earth Planets Space, 65, this issue, 1223–1231, 2013.View ArticleGoogle Scholar
- Sabaka, T. J., N. Olsen, and R. A. Langel, A comprehensive model of the near-Earth magnetic field: Phase 3, NASA/TM-2000-209894, 1–75, 2000.Google Scholar
- Sabaka, T. J., N. Olsen, and R. A. Langel, A comprehensive model of the quiet-time, near-Earth magnetic field: Phase 3, Geophys. J. Int., 151, 32–68, doi:10.1046/j.1365-246X.2002.01774.x, 2002.View ArticleGoogle Scholar
- Sabaka, T. J., N. Olsen, and M. E. Purucker, Extending comprehensive models of the Earth’s magnetic field with ϕrsted and CHAMP data, Geophys. J. Int., 159, 521–547, doi:10.1111/j.1365-246X.2004.02421.x, 2004.View ArticleGoogle Scholar
- Sabaka, T. J., L. Tϕffner-Clausen, and N. Olsen, Use of the Comprehensive Inversion method for Swarm satellite data analysis, Earth Planets Space, 65, this issue, 1201–1222, 2013.View ArticleGoogle Scholar
- Schmucker, U., A spherical harmonic analysis of solar daily variations in the years 1964–1965: Response estimates and source fields for global induction—I. Methods, Geophys. J. Int., 136, 439–454, doi:10.1046/j.1365-246X.1999.00742.x, 1999a.View ArticleGoogle Scholar
- Schmucker, U., A spherical harmonic analysis of solar daily variations in the years 1964–1965: Response estimates and source fields for global induction—II. Results, Geophys. J. Int., 136, 455–476, doi:10.1046/j.1365-246X.1999.00743.x, 1999b.View ArticleGoogle Scholar
- Swarm Level 2 Processing System Consortium, Product specification for L2 Products and Auxiliary Products, Doc. no: SW-DS-DTU-GS-0001, 2013.Google Scholar
- Takeda, M., Features of global geomagnetic Sq field from 1980 to 1990, J. Geophys. Res., 107(A9), 1–8, doi:10.1029/2001JA009210, 2002.Google Scholar
- Thébault, E., P. Vigneron, S. Maus, A. Chulliat, O. Sirol, and G. Hulot, Swarm SCARF Dedicated Lithospheric Field Inversion chain, Earth Planets Space, 65, this issue, 1257–1270, 2013.View ArticleGoogle Scholar