Main Field Model Research Articles

Evaluation of candidate geomagnetic field models for IGRF-12

The 12th revision of the International Geomagnetic Reference Field (IGRF) was issued in December 2014 by the International Association of Geomagnetism and Aeronomy (IAGA) Division V Working Group V-MOD ( http://www.ngdc.noaa.gov/IAGA/vmod/igrf.html ). This revision comprises new spherical harmonic main field models for epochs 2010.0 (DGRF-2010) and 2015.0 (IGRF-2015) and predictive linear secular variation for the interval 2015.0-2020.0 (SV-2010-2015). The models were derived from weighted averages of candidate models submitted by ten international teams. Teams were led by the British Geological Survey (UK), DTU Space (Denmark), ISTerre (France), IZMIRAN (Russia), NOAA/NGDC (USA), GFZ Potsdam (Germany), NASA/GSFC (USA), IPGP (France), LPG Nantes (France), and ETH Zurich (Switzerland). Each candidate model was carefully evaluated and compared to all other models and a mean model using well-defined statistical criteria in the spectral domain and maps in the physical space. These analyses were made to pinpoint both troublesome coefficients and the geographical regions where the candidate models most significantly differ. Some models showed clear deviation from other candidate models. However, a majority of the task force members appointed by IAGA thought that the differences were not sufficient to exclude models that were well documented and based on different techniques. The task force thus voted for and applied an iterative robust estimation scheme in space. In this paper, we report on the evaluations of the candidate models and provide details of the algorithm that was used to derive the IGRF-12 product.

POGO satellite orbit corrections: an opportunity to improve the quality of the geomagnetic field measurements?

We present an attempt to improve the quality of the geomagnetic field measurements from the Polar Orbiting Geophysical Observatory (POGO) satellite missions in the late 1960s. Inaccurate satellite positions are believed to be a major source of errors for using the magnetic observations for field modelling. To improve the data, we use an iterative approach consisting of two main parts: one is a main field modelling process to obtain the radial field gradient to perturb the orbits and the other is the state-of-the-art GPS orbit modelling software BERNESE to calculate new physical orbits. We report results based on a single-day approach showing a clear increase of the data quality. That single-day approach leads, however, to undesirable orbital jumps at midnight. Furthermore, we report results obtained for a much larger data set comprising almost all of the data from the three missions. With this approach, we eliminate the orbit discontinuities at midnight but only tiny quality improvements could be achieved for geomagnetically quiet data. We believe that improvements to the data are probably still possible, but it would require the original tracking observations to be found.

Main field and secular variation candidate models for the 12th IGRF generation after 10 months of Swarm measurements

We describe the main field and secular variation candidate models for the 12th generation of the International Geomagnetic Reference Field model. These two models are derived from the same parent model, in which the main field is extrapolated to epoch 2015.0 using its associated secular variation. The parent model is exclusively based on measurements acquired by the European Space Agency Swarm mission between its launch on 11/22/2013 and 09/18/2014. It is computed up to spherical harmonic degree and order 25 for the main field, 13 for the secular variation, and 2 for the external field. A selection on local time rather than on true illumination of the spacecraft was chosen in order to keep more measurements. Data selection based on geomagnetic indices was used to minimize the external field contributions. Measurements were screened and outliers were carefully removed. The model uses magnetic field intensity measurements at all latitudes and magnetic field vector measurements equatorward of 50° absolute quasi-dipole magnetic latitude. A second model using only the vertical component of the measured magnetic field and the total intensity was computed. This companion model offers a slightly better fit to the measurements. These two models are compared and discussed.We discuss in particular the quality of the model which does not use the full vector measurements and underline that this approach may be used when only partial directional information is known. The candidate models and their associated companion models are retrospectively compared to the adopted IGRF which allows us to criticize our own choices.

International Geomagnetic Reference Field: the 12th generation

The 12th generation of the International Geomagnetic Reference Field (IGRF) was adopted in December 2014 by the Working Group V-MOD appointed by the International Association of Geomagnetism and Aeronomy (IAGA). It updates the previous IGRF generation with a definitive main field model for epoch 2010.0, a main field model for epoch 2015.0, and a linear annual predictive secular variation model for 2015.0-2020.0. Here, we present the equations defining the IGRF model, provide the spherical harmonic coefficients, and provide maps of the magnetic declination, inclination, and total intensity for epoch 2015.0 and their predicted rates of change for 2015.0-2020.0. We also update the magnetic pole positions and discuss briefly the latest changes and possible future trends of the Earth’s magnetic field.

NOAA/NGDC candidate models for the 12th generation International Geomagnetic Reference Field

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 five-year 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 IGRF-12. 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.

Geomagnetic main field modeling with DMSP

AbstractThe Defense Meteorological Satellite Program (DMSP) launches and maintains a network of satellites to monitor the meteorological, oceanographic, and solar‐terrestrial physics environments. In the past decade, geomagnetic field modelers have focused much attention on magnetic measurements from missions such as CHAMP, Ørsted, and SAC‐C. With the completion of the CHAMP mission in 2010, there has been a multiyear gap in satellite‐based vector magnetic field measurements available for main field modeling. In this study, we calibrate the special sensor magnetometer instrument on board DMSP to create a data set suitable for main field modeling. These vector field measurements are calibrated to compute instrument timing shifts, scale factors, offsets, and nonorthogonality angles of the fluxgate magnetometer cores. Euler angles are then computed to determine the orientation of the vector magnetometer with respect to a local coordinate system. We fit a degree 15 main field model to the data set and compare with the World Magnetic Model and Ørsted scalar measurements. We call this model DMSP‐MAG‐1, and its coefficients and software are available for download at http://geomag.org/models/dmsp.html. Our results indicate that the DMSP data set will be a valuable source for main field modeling for the years between CHAMP and the recently launched Swarm mission.

Toward a better representation of the secular variation. Case study: The European network of geomagnetic observatories

In the present paper we discuss a few issues regarding the secular variation (SV) and secular acceleration (SA) of the geomagnetic field that have consequences on mapping them at regional scales. Data from the European network of geomagnetic observatories have been analyzed from the perspective offered by existing long time series of annual means. The existence of high-frequency ingredients in the temporal change of the main field has been taken into account too. The importance of eliminating, from observatory and main field model data, prior to any discussion on secular variation, the signal related to external variations is demonstrated. Its consequences for SV analysis and/or mapping, including the jerk concept, are shown. Also, the importance of the geographical scale at which the SV is represented is discussed. To that aim, we used gufm1, IGRF and CM4 models for the main field from which the residual external signature was eliminated. The contribution of high-frequency ingredients to the map pattern is revealed. The results of the paper set additional observational constraints to the main field and geodynamo modeling.

Seasonal and longitudinal variations of the solar quiet (Sq) current system during solar minimum determined by CHAMP satellite magnetic field observations

[1] Vector magnetometer observations from the Challenging Minisatellite Payload (CHAMP) satellite are used to determine the solar quiet (Sq) current system during the recent solar minimum. Observations from 2006 to 2008 are combined, and after removal of a main field model and accounting for field-aligned currents, the longitudinal and seasonal variation of the Sq currents are determined through the method of spherical harmonic analysis. Comparison with Sq currents derived from ground-based magnetometers in the African/European longitude sector reveals similar amplitudes and seasonal variations, indicating that the CHAMP observations can reliably determine the Sq current system. The seasonal variation is consistent with prior observations during solar minimum conditions and in the Northern Hemisphere exhibits a primarily annual variation with peak currents during local summer. The seasonal variation in the Southern Hemisphere is characterized by a semiannual variation with the maxima occurring around the equinoxes. Significant longitudinal variations are also observed, and they display a seasonal variability. During Northern Hemisphere summer, the predominant feature at local noon is a wave number 1 variation in longitude. During the remainder of the year, a wave 3 longitudinal structure is observed at this local time. The longitudinal variations are considered to be due to a combination of the orientation and strength of the geomagnetic field as well as the tidal winds in the lower thermosphere. Variations in tidal winds due to nonmigrating tides may influence the dynamo-generated electric fields and currents, resulting in the observed longitudinal variations of the Sq current function.

International Geomagnetic Reference Field: the eleventh generation

The eleventh generation of the International Geomagnetic Reference Field (IGRF) was adopted in December 2009 by the International Association of Geomagnetism and Aeronomy Working Group V-MOD. It updates the previous IGRF generation with a definitive main field model for epoch 2005.0, a main field model for epoch 2010.0, and a linear predictive secular variation model for 2010.0–2015.0. In this note the equations defining the IGRF model are provided along with the spherical harmonic coefficients for the eleventh generation. Maps of the magnetic declination, inclination and total intensity for epoch 2010.0 and their predicted rates of change for 2010.0–2015.0 are presented. The recent evolution of the South Atlantic Anomaly and magnetic pole positions are also examined.

Magnetic properties and Archeointensity of Earth’s magnetic field recovered from El Opeño, earliest funeral architecture known in Western Mesoamerica

Despite of the impressive cultural heritage and abundant archaeological sites, absolute geomagnetic intensity data from Mesoamerica are still sparse. Archeointensity determinations using the Coe variant of the Thellier and Thellier method have been carried out on some selected pottery fragments from the El Openo archeological site which has the earliest funeral architecture known in western Mesoamerica. The El Openo chronology is supported by six C 14 datings performed on carbon-bearing materials. Detailed rock magnetic experiments including susceptibility vs. temperature curves, hysteresis cycles and thermal demagnetization procedures were carried out in order to estimate the magnetic carriers and their stability. Cooling rate and anisotropy remanence corrected intensity values range from 25.0 ± 2.3 to 40.2 ± 3.0 µT and corresponding virtual axial dipole moments (VADM) range from 5.6 ± 0.5 to 8.9 ± 0.7  10 22 Am 2 . In addition, we present here a new compilation and analysis of existing absolute intensity data in order to try to estimate the variation of the Earth’s magnetic field over the past three millennia. The mean archeointensity obtained in the present study agrees reasonably well with the predicted absolute intensities retrieved from the CALS7K main field model. Other available Mesoamerican data, however, differ from this model. Most of available archeointensity data from Mesoamerica agree reasonably well with the ARCH3K main field model prediction. The broad peak defined at about 50 A.D. by our data is also predicted by the CALS3k.3 main field model but slightly displaced to the right

Candidate models for the IGRF-11th generation making use of extrapolated observatory data

Three candidate models are produced in response to the call for IGRF-11 models. A main field model around epoch 2005.0 is based on one year of Orsted and CHAMP measurements, and is proposed for the definitive model for epoch 2005.0. A main field model around epoch 2009.5, based on two months of CHAMP measurements and extrapolated to 2010.0, is proposed as a main field model for epoch 2010.0. A secular variation model valid for 2010.0–2015.0, based on the extrapolation through exponential smoothing of observatory monthly mean values, is proposed as a predictive secular variation model. Comparison of similar extrapolations made for previous IGRF generations with actual observations are presented and discussed.

Evaluation of candidate geomagnetic field models for IGRF-11

The eleventh generation of the International Geomagnetic Reference Field (IGRF) was agreed in December 2009 by a task force appointed by the International Association of Geomagnetism and Aeronomy (IAGA) Division V Working Group V-MOD. New spherical harmonic main field models for epochs 2005.0 (DGRF-2005) and 2010.0 (IGRF-2010), and predictive linear secular variation for the interval 2010.0–2015.0 (SV-2010-2015) were derived from weighted averages of candidate models submitted by teams led by DTU Space, Denmark (team A); NOAA/NGDC, U.S.A. (team B); BGS, U.K. (team C); IZMIRAN, Russia (team D); EOST, France (team E); IPGP, France (team F); GFZ, Germany (team G) and NASA-GSFC, U.S.A. (team H). Here, we report the evaluations of candidate models carried out by the IGRF-11 task force during October/November 2009 and describe the weightings used to derive the new IGRF-11 model. The evaluations include calculations of root mean square vector field differences between the candidates, comparisons of the power spectra, and degree correlations between the candidates and a mean model. Coefficient by coefficient analysis including determination of weighting factors used in a robust estimation of mean coefficients is also reported. Maps of differences in the vertical field intensity at Earth’s surface between the candidates and weighted mean models are presented. Candidates with anomalous aspects are identified and efforts made to pinpoint both troublesome coefficients and geographical regions where large variations between candidates originate. A retrospective analysis of IGRF-10 main field candidates for epoch 2005.0 and predictive secular variation candidates for 2005.0–2010.0 using the new IGRF-11 models as a reference is also reported. The high quality and consistency of main field models derived using vector satellite data is demonstrated; based on internal consistency DGRF-2005 has a formal root mean square vector field error over Earth’s surface of 1.0 nT. Difficulties nevertheless remain in accurately forecasting field evolution only five years into the future.

IGRF candidate models at times of rapid changes in core field acceleration

We submit three candidate models following the call for IGRF-11. We apply a simple modeling approach in spherical harmonics based on a quadratic Taylor expansion for the internal field time variations. We use the Dst magnetic index as a proxy for the external field variations. In order to compensate for the limitations incurred by such a conventional approach, we focus on the optimal selection of satellite data in space and time. We also show that some a priori knowledge about the core field state helps us to avoid the pitfall encountered in the case of rapid changes of core field accelerations. Indeed, various acceleration events of relevance for the IGRF 11th occurred between 2003 and 2010, one of them being a geomagnetic jerk. They could entail disagreements between IGRF candidate models for the secular variation (SV) if data prior to 2008 are used. Our SV and main field (MF) candidate models have a root mean square uncertainty less than 6 nT/yr and 8 nT, respectively, with respect to the modeled magnetic field contributions. These values correspond to the intrinsic error associated with truncating SV and MF models to spherical harmonic degree 8 and 13, respectively, as requested for IGRF models.

ITalian Geomagnetic Reference Field (ITGRF): update for 2000 and secular variation model up to 2005 by autoregressive forecasting

The updated version of the ITalian Geomagnetic Reference Field (ITGRF) for 2000.0 and its secular variation model up to 2005.0 are presented in this paper. The main field model is based on a simple polynomial approximation in latitude and longitude of the geomagnetic field elements computed from IGRF on a 12° ¥ 11° grid centred over Italy. The annual means from L’Aquila observatory were used to determine the baseline level, imposing a constant observatory anomaly bias. This procedure gives a set of 6 coefficients every 5 years from 1960 to 2005 for the horizontal H, total field F, vertical Z and declination D elements of the geomagnetic field. The extrapolation of ITGRF to 2005 is based on an autoregressive forecasting of the L’Aquila observatory annual means. Comparison of the field values computed from the model with those recorded at the other Italian observatory (Castello Tesino) shows that the ITGRF improves the fit of the secular variation pattern with respect to the global IGRF model by a factor of 3. The ITGRF represents a reliable alternative to global models when reducing magnetic surveys to a common reference epoch over the Italian region.

Can core‐surface flow models be used to improve the forecast of the Earth's main magnetic field?

Geomagnetic main field models used for navigation are updated every 5 years and contain a forecast of the geomagnetic secular variation for the upcoming epoch. Forecasting secular variation is a difficult task. The change of the main magnetic field is thought to be principally due to advection of the field by flow at the surface of the outer core on short timescales and when large length scales are considered. With accurate secular variation (SV) and secular acceleration (SA) models now available from new satellite missions, inverting for the flow and advecting it forward could lead to a more accurate prediction of the main field. However, this scheme faces two significant challenges. The first arises from the truncation of the observable main field at spherical harmonic degree 13. This can however be handled if the true core flow is large scale and has a rapidly decaying energy spectrum. The second is that even at a given single epoch the instantaneous SV and SA cannot simultaneously be explained by a steady flow. Nevertheless, we find that it may be feasible to use flow models for an improved temporal extrapolation of the main field. A medium‐term (≈10 years) hindcast of the field using a steady flow model outperforms the usual extrapolation using the presently observed SV and SA. On the other hand, our accelerated, toroidal flow model, which explains a larger portion of the observed average SA over the 2000–2005 period, fails to improve both the short‐term and medium‐term hindcasts of the field. This somewhat paradoxical result is related to the occurrence of so‐called geomagnetic jerks, the still poorly known dynamical nature of which remains the main obstacle to improved geomagnetic field forecasts.

Magnetic perturbations seen by CHAMP and evaluated using the TIE-GCM

Abstract. The Thermosphere-Ionosphere Electrodynamics General Circulation Model (TIE-GCM) is a self-consistent, global, atmospheric model that can be used to estimate magnetic perturbations at satellite altitude. These computed perturbations can then be compared with the magnetic vector data provided by low-earth orbiting satellites. In this initial study, the quietest day of each month from 2001–2005 was selected for comparison. CHAMP magnetic vector residuals were computed for these intervals using the CHAOS model to remove core and crustal geomagnetic contributions. Under various input parameters, the TIE-GCM predictions were compared with the CHAMP residuals on an orbit by orbit basis. Initial results demonstrate a reasonable agreement between the TIE-GCM estimates and the CHAMP residuals in non-polar, dayside regions (±50° magnetic latitude) where both are able to resolve the Equatorial Electro-Jet (EEJ) and solar quiet (Sq) current systems. Although no clear component or temporal correlation was discerned, evidence showing the decrease in residual comparisons presents the possibility of using the TIE-GCM to pre-process geomagnetic data for main field modeling purposes.

Representation of the main geomagnetic field using Maxwell's theory of poles

SUMMARY The spatio-temporal variations in the main geomagnetic field are analysed using Maxwell's source representation of the potential function defined by Maxwell's theory of poles. Maxwell sources up to order 4 are obtained for three main geomagnetic field models. The temporal variations in the main geomagnetic field are shown in terms of the variations in the parameters defined in Maxwell's source representation, for example, the Maxwell moments, the Maxwell axes, the intrinsic energy of the Maxwell source, etc. The characteristics of these variations are discussed. Applications of Maxwell's source representation of the potential function to the studies of the earth's magnetic field are suggested.

Search for magnetically quiet CHAMP polar passes and the characteristics of ionospheric currents during the dark season

Abstract. The magnetic activity at auroral latitudes is strongly dependent on season. During the dark season, when the solar zenith angle in the polar region is larger than 100° at all local times, the ionospheric conductivity is much reduced, and generally low activity is encountered. These time intervals are of special interest for the main field modelling, because then the geomagnetic field readings, in particular the field magnitude, are only slightly affected by ionospheric currents. Based on CHAMP data, this study examines how these quiet periods are reflected in the different magnetic field components. The peak FAC density is used as a possible proxy for the deviation of the total field. As a second option, the transverse field component, which is aligned with the auroral oval, is investigated, because it presents a measure for the FAC total current. Correlation analyses with the scalar residuals are performed and both proxies are tested for their suitability of predicting the intensity of the auroral electrojet during the dark polar seasons. The indicators based on the local FAC strength or on the amplitude of the transverse component show a reasonable correlation with the electrojet intensity for these periods, but fail when limited to small amplitudes. The predictability improves considerably if the time sector is limited to dayside hours (08:00–16:00 MLT). As the activity at high latitudes is strongly controlled by the solar wind input, we also consider IMF quantities which may support very quiet conditions. Correlations of the magnetic field scalar residuals with the merging electric field are strongest if only passes in the dayside sector are considered. Best selection results for quiet passes are obtained by combining four conditions: dark season, small average merging electric field, Em<0.8 mV/m, absence of peak values of Em>1.2 mV/m during a time interval of 40 min centred at the polar crossing, and limitation to the dayside sector (08:00–16:00 MLT). The set of quiet polar passes identified by these criteria may be used beneficially in crustal field modelling of the polar regions.

Equatorial electrojet as a diagnostic tool of geomagnetic field models

Abstract The equatorial electrojet (EEJ) is a unique feature of the Earth’s external current systems because it must flow along the dip equator. This provides us with a tool to determine the nature of the variations imposed by competing main field models on the equatorial region. First we show that for certain regions a comparison between scalar geomagnetic measurements that use different models to remove the main field may not be reasonable. Next we found the intrinsic error in the determination of the possible location of the dip equator was ±9.8 km (0.088°) at 108 km altitude for the models shown here. Using scalar measurements from over 14,000 CHAMP satellite passes, the latitude of the maximum of the EEJ field at the satellite altitude was determined by subtracting four different models of the main field. We find that the location can be statistically determined to within ±0.5° of the dip equator (calculated at 108 km altitude) irrespective of longitude, time of the measurement, degree of magnetic activity, and subtracted model. However, variations of the latitude of the maximum EEJ field with longitude are sometimes caused by the actual model and are not always a physical phenomenon. By choosing one model, and assuming it is the best representation of the main field, we have also shown that the accuracy of determination of the position of the EEJ signal is reduced in the morning and evening hours and that a morning and evening shift in the location of the EEJ found using ground measurements is also seen here. There exists a clear annual variation in the position of the EEJ regardless of longitude: it is south of the dip equator in December which is in agreement with the findings of all previous studies.

Deriving main field and secular variation models from synthetic Swarm satellite and observatory data

Abstract We investigate how well the core field component of the underlying model used in the Swarm End-to-End simulator can be recovered when relatively simple geomagnetic field models are fitted to synthetic Swarm satellite and observatory data. In particular we demonstrate the potential benefits of Swarm by deriving models without these data. From two years of observatory data, the underlying secular variation model is recovered up to about spherical harmonic degree 8. This maximum degree is higher than was expected but increases to 10 when satellite data are also used. The constant part of the geomagnetic field model is recovered to at least degree 17. These results improve when a better statistical treatment of the data errors is made, a slightly more complex field model is fitted, or when five years of data are used.