F. J. Lowes

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.

Evaluation of candidate geomagnetic field models for IGRF-12

BackgroundThe 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).FindingsThe 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.ConclusionsThe 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.

New parameterization of external and induced fields in geomagnetic field modeling, and a candidate model for IGRF 2005

When deriving spherical harmonic models of the Earth’s magnetic field, low-degree external field contributions are traditionally considered by assuming that their expansion coefficient q10 varies linearly with the Dst-index, while induced contributions are considered assuming a constant ratio Q1 of induced to external coefficients. A value of Q1 = 0.27 was found from Magsat data and has been used by several authors when deriving recent field models from Èrsted and CHAMP data. We describe a new approach that considers external and induced field based on a separation of Dst = Est + Ist into external (Est) and induced (Ist) parts using a 1D model of mantle conductivity. The temporal behavior of q10 and of the corresponding induced coefficient are parameterized by Est and Ist, respectively. In addition, we account for baseline-instabilities of Dst by estimating a value of q10 for each of the 67 months of Èrsted and CHAMP data that have been used. We discuss the advantage of this new parameterization of external and induced field for geomagnetic field modeling, and describe the derivation of candidate models for IGRF 2005.

An estimate of the errors of the IGRF/DGRF fields 1945–2000

The IGRF coefficients inevitably differ from the true values. Estimates are made of the their uncertainties by comparing IGRF and DGRF models with ones produced later. For simplicity, the uncertainties are summarized in terms of the corresponding root-mean-square vector uncertainty of the field at the Earth’s surface; these rms uncertainties vary from a few hundred to a few nanotesla. (It is assumed that the IGRF is meant to model the long-wavelength long-period field of internal origin, with no attempt to separate the long-wavelength fields of core and crustal origin; the models are meant for users interested in the field near and outside the Earth’s surface, not for core-field theoreticians.) So far we have rounded the main-field coefficients to 1 nT; this contributes an rms vector error of about 10 nT. If we do in fact get a succession of vector magnetic field satellites then we should reconsider this rounding level. Similarly, for future DGRF models we would probably be justified in extending the truncation from n = 10 to n = 12. On the other hand, the rounding of the secular variation coefficients to 0.1 nT could give a false impression of accuracy.

Evaluation of candidate geomagnetic field models for the 10th generation of IGRF

The recent satellite magnetic missions, combined with high quality ground observatory measurements, have provided excellent data for main field modelling. Four different groups submitted seven main-field and eight secular-variation candidate models for IGRF-10. These candidate models were evaluated using several different strategies. Comparing models with independent data was found to be difficult. Valuable information was gained by mapping model differences, computing root mean square differences between all pairs of models and between models and the common mean, and by studying power spectra and azimuthal distributions of coefficient power. The resulting adopted IGRF main-field model for 2005.0, an average of three selected candidate models, is estimated to have a formal root mean square error over the Earth’s surface of only 5 nT, though it is likely that the actual error is somewhat larger than this. Due to the inherent uncertainty in secular variation forecasts, the corresponding error of the adopted secular-variation model for 2005.0–2010.0, an average of four selected candidate models, is estimated at 20 nT/a.

Ninth generation international geomagnetic reference field released

The coefficients for the new 9th Generation International Geomagnetic Reference Field (IGRF) were finalized at the XXIII General Assembly of the International Union of Geophysics and Geodesy (IUGG), held in Sapporo, Japan, in July 2003. The IGRF is widely used as a mathematical representation for the Earths magnetic field in studies of the Earths deep interior, crust, and ionosphere and magnetosphere. It is the product of a collaborative effort between magnetic field modelers and the institutes involved in collecting and disseminating magnetic field data from observatories and surveys around the world and from satellites.

Magnetic Fields on British Trains

People on trains can be exposed to static and alternating magnetic fields which are higher than background levels in most homes and many workplaces. Quantification of such exposure may be of interest for epidemiological purposes but it is also important to ensure that exposure guidelines are complied with. This article describes the types of electric trains and trams in use in the UK and the results of measurements of static and alternating magnetic flux density. Many of the data have been supplied by the operators of the systems described. The measurements summarised in this article are indicative of the magnitudes of magnetic field exposures to be encountered on British trains, but without concomitant frequency information, they are not sufficient to allow demonstration of compliance with exposure standards.

Ionospheric and induced field leakage in geomagnetic field models, and derivation of candidate models for DGRF 1995 and DGRF 2000

As part of the 9th generation of the IGRF defined by IAGA, we proposed a candidate model for DGRF 1995 and two candidate models for DGRF 2000. These candidate models, the derivation of which is described in the present note, are based on the “Comprehensive Model, Version 4 (CM4)”, and on the “Ørsted Main and Secular Variation Model (OSVM)”; two parent models that have been published elsewhere (Olsen, 2002; Sabaka et al., 2004; Lowes and Olsen, 2004). However, the main field part of OSVM is contaminated by “leakage” of the ionospheric field and its induced counterpart, which affects mainly the zonal coefficients g10, g30, …, by 1–2 nT. We describe the reason for this contamination, and present a method to correct for it. Since not only OSVM, but probably all main field models that are derived primarily from data around local midnight suffer from this effect, the presented scheme can also be applied to approximately correct these models.

Spherical Cap Harmonics Revisited and their Relationship to Ordinary Spherical Harmonics

Abstract The “global” representation of the geomagnetic field in terms of ordinary spherical harmonics (SHs) and its corresponding set {g,h} of coefficients has been studied extensively, but the “local” representation in terms of spherical cap harmonics (SCHs) and its corresponding set {G,H} of coefficients is not yet well understood. This paper clarifies some of the main properties of the SCHs and their proper use along with their relationship with the SHs. In particular, it shows that for the spherical cap part of a global field specified by spherical harmonics there is a strict relation between the ordinary Legendre functions of the global representation and the fractional functions of the local expansion; hence we can express the set of coefficients {G,H} in terms of the set {g,h}. Finally, some attention will be given to the role of the leading (n = 0, m = 0) term of the SCH expansion.

Optimum use of satellite intensity and vector data in modelling the main geomagnetic field

Abstract Monte Carlo simulation has been used to investigate the optimum use of Magsat-type intensity and vector data in producing spherical harmonic models of the main geomagnetic field. As is well known, using only intensity data gives large vector errors in the model field, particularly in the equatorial region. Adding (or substituting) quite small amounts of vector data in the equatorial region very much improves the model. Adding more vector data gives a bit more improvement, but polewards of about 30° latitude it is better to use good (small variance) intensity data rather than poor (large variance) vector data. By making better use of the existing data it should be possible to reduce the errors of the GSFC (12/83) model by a factor of about three.