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NOAA/NGDC candidate models for the 12th generation International Geomagnetic Reference Field
 Patrick Alken^{1, 2}Email author,
 Stefan Maus^{1, 2},
 Arnaud Chulliat^{1, 2} and
 Chandrasekharan Manoj^{1, 2}
https://doi.org/10.1186/s4062301502151
© Alken et al.; licensee Springer. 2015
 Received: 30 January 2015
 Accepted: 19 March 2015
 Published: 12 May 2015
Abstract
The International Geomagnetic Reference Field (IGRF) is a model of the geomagnetic main field and its secular variation, produced every 5 years from candidate models proposed by a number of international research institutions. For this 12th generation IGRF, three candidate models were solicited: a main field model for the 2010.0 epoch, a main field model for the 2015.0 epoch, and the predicted secular variation for the fiveyear period 2015 to 2020. The National Geophysical Data Center (NGDC), part of the National Oceanic and Atmospheric Administration (NOAA), has produced three candidate models for consideration in IGRF12. The 2010 main field candidate was produced from Challenging Minisatellite Payload (CHAMP) satellite data, while the 2015 main field and secular variation candidates were produced from Swarm and Ørsted satellite data. Careful data selection was performed to minimize the influence of magnetospheric and ionospheric fields. The secular variation predictions of our parent models, from which the candidate models were derived, have been validated against independent ground observatory data.
Keywords
 Geomagnetic field
 Magnetic field modeling
 IGRF
 Swarm
Background
The Earth’s geomagnetic field is generated by a variety of sources. The primary source, known as the main field, is produced by the convection of liquid iron in the Earth’s outer core. Additional sources include magnetized structures in the Earth’s crust, as well as electric current systems flowing in the ionosphere and magnetosphere. The International Geomagnetic Reference Field (IGRF) is a standard representation of the Earth’s geomagnetic main field and its secular variation, which is the temporal change of the magnetic field on time scales of 1 year or more. The IGRF is produced by an international collaborative effort and is updated every 5 years. For this 12th generation IGRF, models were solicited from the international community for a retroactive update of the main field for 2010.0, a description of the main field for 2015.0, and the predicted secular variation of the main field for 2015.0 to 2020.0. Retroactive updates of the IGRF, such as the current call for 2010, are named as the Definitive Geomagnetic Reference Field (DGRF), as it is possible to make use of more data around that epoch which was not available at the time of the original model release, and it is typically not planned to issue further updates of these past epochs.
While the IGRF is intended to describe the largescale, long wavelength part of the internal geomagnetic field, during the modeling process, it is necessary to carefully account for and parameterize the other sources so their effects can be separated from the final IGRF model. This usually involves careful data selection during geomagnetically quiet times to minimize the influence of external fields, parameterizing the steady ringcurrent field flowing in the magnetosphere and fitting the data to higher degree parent models, which would include shorter wavelength contributions from the Earth’s magnetized crust. The final IGRF candidates are then extracted from these parent models by truncating the model expansions, most often parameterized by spherical harmonics, to the desired spatial resolution.
In this paper, we describe the three National Geophysical Data Center (NGDC) candidate models for IGRF12. Each candidate model was taken from a more extensive parent model, which attempted to parameterize the other various field sources described above. In section ‘Candidate for the 2010 DGRF’, we describe the parent model for our 2010 DGRF candidate. The methodology behind this model parameterization has been discussed in some detail in Maus et al. (2010) and Chulliat and Maus (2014), and so we only briefly review the main steps in producing the model. In section ‘Main field and secular variation candidates for IGRF 2015’, we discuss our candidate models for the 2015 IGRF main field and secular variation, which were both extracted from the same parent model. For these models, we used a similar methodology to the 2010 DGRF; however, there are some differences in the data selection and model parameterization, and the underlying data sets rely on different satellites, and so we provide a more complete discussion of these two models.
Methods
Candidate for the 2010 DGRF
 1.
Dst index magnitude does not exceed 30 nT at all latitudes.
 2.
\(\left  \frac {d}{dt} Dst \right  \le \) 2 nT/h at mid latitudes, 5 nT/h at high latitudes.
 3.
a _{ m } index less than 12 at mid latitudes, 27 at high latitudes.
 4.
a _{ m } 3 h previous less than 15 at mid latitudes, 27 at high latitudes.
 5.
Interplanetary magnetic field components: B _{ y }≤ 8 nT, −2≤B _{ z }≤6 nT.
 6.
E _{ m }≤0.8 mV/m.
 7.
In the mid latitude region, vector and scalar data between 0500 and 2000 local time were discarded. At high latitudes, no vector data is used, but scalar data at all local times is included.
For each of the models used in the study of Chulliat and Maus (2014), the Gauss coefficients of the magnetic scalar potential were parameterized as a second order Taylor series in time, with the first derivative corresponding to the linear secular variation and the second derivative corresponding to the secular acceleration. Models were computed using a sliding window which included 3 years of CHAMP data. While a 3year window introduces some time averaging of the resulting coefficients, it was found that this length was necessary to obtain stable estimates of the secular variation and secular acceleration parameters. Damping was applied to the secular variation coefficients above degree 13 and secular acceleration coefficients above degree 8. All coefficients were estimated using least squares minimization of the data residuals. The latest model estimated from this method had an epoch of 2009.17. For our final DGRF candidate, we extrapolated the main field coefficients to epoch 2010.0 using the secular variation and secular acceleration coefficients and the second order Taylor series relation. Since this modeling method has been reported previously, we refer the reader to Maus et al. (2010) for further discussion and plots of the model residuals and their statistics.
Main field and secular variation candidates for IGRF 2015
For the 2015.0 epoch, NGDC has produced candidate models for both the main field and secular variation.
Data sources
We exclusively used satellite observations from the Ørsted and Swarm missions to construct our IGRF candidate models for the 2015.0 epoch. Ørsted (Olsen et al. 2003) was launched in February 1999 into an elliptical nearpolar orbit with an inclination of 96.4°. Its current perigee and apogee are about 635 and 835 km, respectively, and its orbital period is about 99.5 min. Ørsted has been providing only scalar field measurements since 2005 due to a star camera failure. It has furthermore ceased providing data after June 2013. While only half a year of scalar data from Ørsted was available in 2013, we found that including this data in the modeling helped to resolve the higher degree secular variation coefficients.
The Swarm satellite mission (FriisChristensen et al. 2006) is composed of three satellites which were launched in November 2013 into nearpolar orbits. Each Swarm satellite carries a vector fluxgate magnetometer (VFM) instrument in addition to an absolute scalar magnetometer (ASM) (Leger et al. 2009) which provides the scalar reference for calibrating the vector measurement. A lower pair of satellites (Alpha and Charlie) fly in a sidebyside constellation with an inclination of 87.4° and an altitude of about 465 km. The third satellite (Bravo) flies in a higher orbit of about 520 km with an inclination of 88°.
Data selection

Flags_F < 64 (ASM instrument recorded data)

Flags_B < 255 (VFM instrument recorded data)

Flags_q < 31 (at least 2 star cameras operational)
 1.
Dst index magnitude does not exceed 30 nT.
 2.
Interplanetary magnetic field components: B _{ y }≤8 nT, −2≤B _{ z }≤6 nT.
 3.
Ap index less than 12 below 60° geomagnetic latitude.
 4.
Ap index less than 27 above 60° geomagnetic latitude.
 5.
Local times between 0500 and 2200 are excluded below 60° geomagnetic latitude for Swarm data. For Ørsted, we exclude local times between 0500 and 2000, since the satellite is near a 9 am/9 pm orbit for the spring of 2013.
 6.
Above 60° geomagnetic latitude, the sun must be at least 10° below the horizon to ensure darkness.
 7.
Vector data (from Swarm) is used only below 55° geomagnetic latitude to reduce contamination from highlatitude ionospheric current systems. Scalar data (from Swarm and Ørsted) is used at all latitudes.
Model parameterization
i.e., along the internal dipole direction. The values 0.7 and 0.3 are approximate relative strengths of the external and induced fields (Maus and Weidelt 2004).
where a _{ij},n _{ij} are the area on a unit sphere and number of measurements for bin (i,j), respectively. This expression effectively upweights sparsely sampled regions with larger areas (typically low latitudes) and downweights densely sampled regions with smaller areas (typically at the poles). K is a normalization constant chosen so that \(\sum _{\text {ij}} w_{\text {ij}} = 1\). At each step of the iteration, these initial weights are multiplied by the Huber weights to produce the final weights.
Results and discussion
Residual statistics of satellite measurements against parent model
Swarm A  Swarm B  Swarm C  Ørsted  

Mean  Rms  Mean  Rms  Mean  Rms  Mean  Rms  
B _{ x }  0.04  3.81  0.14  4.00  0.29  4.01  
B _{ y }  0.11  3.33  0.08  3.32  0.15  3.35  
B _{ z }  0.07  1.81  0.04  2.07  0.12  2.06  
Lowlatitude B  0.01  2.59  0.08  2.60  0.09  2.64  0.56  5.16 
Highlatitude B  0.84  11.79  1.26  11.14  1.20  11.88  1.94  15.59 
Candidate models
After the parent model was estimated from the satellite data, we truncated it to spherical harmonic degree 13 for the main field and degree 8 for the secular variation, as specified in the IGRF call. We found that using 10 months of Swarm data alone was only able to provide an undamped estimate of the secular variation (SV) to degree 6. Including the 6 months of Ørsted data in 2013 allows an undamped SV estimate to degree 11. Since the parent model was computed for the epoch 2014.3, we advanced the main field coefficients to 2015.0 using the linear secular variation. The secular variation coefficients remained unchanged since we did not include higher order time derivatives in the model.
Validation with ground observatories
Comparison of IGRF11 and our IGRF12 candidate SV models with spline fits to 66 observatories
dX/dt (nT/year)  dY/dt (nT/year)  dZ/dt (nT/year)  

Mean  Rms  Mean  Rms  Mean  Rms  
IGRF11  8.96  14.20  1.25  9.93  3.85  18.15 
IGRF12 candidate  11.82  10.31  1.19  4.77  2.12  7.91 
We found that the candidate SV model for 2015.0 was in agreement with the latest trends of the SV at each observatory. For example, at KOU, the latest data available show a strong acceleration of the azimuthal component after 2012 which is captured by our 2015.0 SV model. At MBO, the model is further away from the observatory data on both the azimuthal and radial component, but is in agreement with a reasonable extrapolation of the SV trends before 2014. We also check that the 2010 SV model is in very good agreement with the selected observatory data, despite the extrapolation from 2009.17 to 2010.0. As this validation is made retrospectively, i.e., after acquiring enough observatory data to recover the SV around 2010.0, this gives us confidence in the extrapolation applied to the 2015.0 SV candidate. This figure also illustrates the effect of the truncation of an SV model from degree 13 to degree 8; the prediction from the truncated degree 8 SV at 2010.0 are a few (less than 5) nT/year away from the SV measured at the selected observatories. Finally, the average SV in 2012.5 is found to be in agreement with the average SV from observatory data over 2010 to 2015 thus further validating our main field candidate models. Similar results were found at the other four observatories. None of our candidate models included observatory data in their calculation; therefore, this analysis represents a test against truly independent data.
Conclusions
The National Geophysical Data Center at National Oceanic and Atmospheric Administration (NOAA) has produced three candidate models for the 12th generation IGRF. We provide a 2010 DGRF main field candidate based on CHAMP satellite data, a 2015 IGRF main field candidate and a 2015 to 2020 secular variation candidate based on Swarm and Ørsted satellite data. These candidates were all derived from sophisticated parent models which include careful data selection, high degree crustal field parameterization, and external magnetospheric field corrections. The resulting models were truncated to spherical harmonic degree 13 for the main field and degree 8 for the secular variation. All three candidate models have been successfully validated against independent ground observatory data.
Declarations
Acknowledgements
The support of the CHAMP mission by the German Aerospace Center (DLR) and the Federal Ministry of Education and Research is gratefully acknowledged. The Ørsted mission was extensively supported by the Danish Government, NASA, ESA, CNES, and DARA. The authors acknowledge ESA for providing access to the Swarm L1b data. The results presented in this paper rely on data collected at magnetic observatories. We thank the national institutes that support them and INTERMAGNET for promoting high standards of magnetic observatory practice (www.intermagnet.org).
Authors’ Affiliations
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