Summary

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.

Introduction

The International Geomagnetic Reference Field (IGRF) is an established numerical model used to calculate the large scale, internal, part of the Earth's magnetic field at times between 1900.0 A.D. and present, at locations on or above Earth's surface. It is produced and maintained by a team of geomagnetic field modellers under the auspices of the International Association of Geomagnetism and Aeronomy (IAGA) Working Group V-MOD and is derived from observations collected by satellites, at magnetic observatories, and during magnetic surveys. It is used by scientists (e.g. in studies of space weather or in investigations of local magnetic anomalies) and also by commercial organizations and private individuals who often use the geomagnetic field as a source of orientation information.

The internal part of the geomagnetic field, which is almost entirely core-generated, undergoes slow, but noticeable, changes on timescales of years to decades. Consequently the IGRF must be revised, typically every five years, to remain up to date and as accurate as possible; Table 1 summarizes details of previous generations of the IGRF. Each generation consists of a series of constituent models at 5-yr intervals, each one of which is designated definitive or non-definitive. Once a constituent model is designated definitive it is called a Definitive Geomagnetic Reference Field (DGRF) and it is not revised in subsequent generations of the IGRF. The non-definitive constituent models are referred to as IGRF models. Note that DGRF models have been produced only for epochs from 1945.0 onwards. For further details concerning the history of the IGRF readers should consult Barton (1997), Maus et al. (2005a) or Macmillan & Finlay (2010); here attention will focus on the latest (11th generation) revision. Legacy versions of the IGRF are now available from the online archive located at http://www.ngdc.noaa.gov/IAGA/vmod/igrf_old_models.html. These may be useful, for example, to workers who know that a previous generation IGRF has been subtracted from their data and who wish to recover the original data or recorrect it with a more recent reference field.

Table 1

Summary of IGRF generations, their intervals of validity and related references.

Table 1

Summary of IGRF generations, their intervals of validity and related references.

The 11th generation of the IGRF (hereafter IGRF-11) was agreed in December 2009 by a task force of IAGA Working Group V-MOD. The purpose of this note is to document the release of IGRF-11, to act as a permanent published record of model coefficients and to briefly describe the large-scale features of the present geomagnetic field at Earth's surface as revealed by the updated model.

Mathematical Formulation of the IGRF Model

On and above the Earth's surface, the IGRF model represents the geomagnetic field B(r, θ, φ, t) produced by internal sources in terms of a scalar potential V(r, θ, φ, t). We then have B=−∇V where V is a finite series having the numerical Gauss coefficients gmn, hmn (conventionally given in units of nanotesla, hereafter nT):  

1
formula
Here r denotes the radial distance from the centre of the Earth in units of km, a= 6371.2 km is the magnetic reference spherical radius which is close to the mean Earth radius, θ denotes geocentric co-latitude (i.e. 90°− latitude), and φ denotes east longitude. When converting between geocentric and geodetic coordinates, it is recommended to use the World Geodetic System 1984 datum and spheroid (major axis A of 6378.137 km and a reciprocal flattening 1/f of 298.257223563). Pmn (cos θ) are the Schmidt semi- (or quasi-) normalized associated Legendre functions of degree n and order m (see, e.g. Winch et al. 2005). The maximum spherical harmonic degree of the expansion N is chosen so that the coefficients of the model are reliably determined given the available coverage and quality of observations. For IGRF-11, N was chosen to be 10 up to and including epoch 1995.0, thereafter it is extended to degree 13 to take advantage of the excellent data provided by the Ørsted and CHAMP satellites.

In the IGRF model, Gauss coefficients gmn and hmn are provided for the main field (MF) at epochs separated by 5-yr intervals between 1900.0 and 2010.0 A.D. The time-dependence of the Gauss coefficients is then specified using the following linear expression:  

2
formula
and similarly for hmn. Here t is the time of interest (in units of years) and T0 is the epoch preceding t which is an exact multiple of 5 yr, such that T0t < (T0+ 5.0). The coefficients graphic, given in units of nT yr−1, denote the average first time derivative of gmn(t) during the interval T0 to T0+ 5.0, i.e. the linear secular variation (SV) during this interval. When MF models exist for both T0 and T0+ 5.0 then graphic is simply calculated using linear interpolation as [gmn(T0+ 5.0) −gmn(T0)]/5.0. For the final 5 yr of the model validity (between 2010.0 and 2015.0 for IGRF-11) coefficients of predictive average SV graphic and graphic are explicitly provided.

The geocentric components of the geomagnetic field in the northward, eastward and radially inwards directions (X′, Y′ and Z′) are obtained from the model coefficients using eq. (1) and by taking appropriate components of the gradient of V in spherical polar coordinates,  

3
formula

It is often necessary to work in geodetic coordinates and to use the World Geodetic System 1984 datum defined above. Transformations from geocentric to geodetic coordinates and from the geocentric field components (X′, Y′, Z′) into the geodetic field components (X, Y, Z) are described by eqs (1)–(4) of Hulot et al. (2007). Often the declination D, inclination I, the horizontal intensity H and the total intensity F are required for applications; these are obtained from X, Y and Z using the relations,  

4
formula

The 11th Generation IGRF

In May 2009, the IGRF-11 task force appointed by IAGA Division V-MOD issued a call for candidate models. Candidates for the Definitive Geomagnetic Reference Field (DGRF) for epoch 2005.0, for a provisional IGRF model for epoch 2010.0, and for a predictive SV model for the interval 2010.0–2015.0 were requested. Candidates were received in early October 2009. Seven candidates were submitted for the DGRF epoch 2005.0 and IGRF epoch 2010.0 MF models. Team A was led by DTU Space, Denmark, along with workers from IPGP, France, and GSFC-NASA, USA; Team B was led by NGDC/NOAA, USA together with colleagues from GFZ, Germany; Team C was from BGS, UK; Team D was from IZMIRAN, Russia; Team E was led by EOST, France, with assistance from colleagues at LPGN, IPGP and LATMOS, France; Team F was led by IPGP, France, with input from workers in NGDC/NOAA, USA and LPGN, EOST and LATMOS, France; Team G was from GFZ, Germany. The same teams also contributed candidate predictive SV models and there was one additional SV candidate from Team led by GSFC-NASA, USA, in collaboration with UMBC, USA, and University of Liverpool, UK; in all, eight SV candidates were received.

The MF candidate models had a maximum spherical harmonic degree N= 13, whereas the task force voted to retain a maximum degree of N= 8 for the predictive SV models. The candidate models together with brief descriptions provided by the authors may be obtained from the web page http://www.ngdc.noaa.gov/IAGA/vmod/candidatemodels.html. Papers providing fuller descriptions of the candidate models and detailing the evaluations carried out by the task force (similar to the analysis of the candidates contributing to IGRF-10 carried out by Maus et al. 2005b) will appear in a forthcoming special issue of Earth, Planets and Space.

The final IGRF-11 MF models for epochs 2005.0 and 2010.0 as well as the predictive SV model for 2010.0–2015.0 were calculated using weighted means of the candidates. The weights were agreed by a vote of the IGRF-11 task force based on information gleaned from model evaluations, more details of which are documented in Finlay et al. (2010).

High-quality, globally distributed, observations of the geomagnetic field are essential to the production of an accurate IGRF revision. The collection of the required comprehensive set of observations involves a significant international collaborative effort. The availability of satellite measurements, from the CHAMP (Reigber et al. 2002), Ørsted (Neubert et al. 2001) and SAC-C missions, and observatory measurements (see Table A1 in the appendix) was of fundamental importance to IGRF-11.

Table A1

List of agencies supporting observatories whose data were used in deriving constituent models for IGRF-.

Table A1

List of agencies supporting observatories whose data were used in deriving constituent models for IGRF-.

IGRF-11 remains unchanged from IGRF-10 for epoch 2000.0 and earlier. The model MF coefficients are rounded to 1 nT for epochs between 1900.0 and 1995.0; to 0.1 nT for epochs 2000.0 and 2010.0, and to 0.01 nT for DGRF 2005.0 reflecting the increasing consistency of the candidate models (Finlay et al. 2010). The predictive SV coefficients are rounded to the nearest 0.1 nT yr−1. Note that although the formal root mean square (rms) error in DGRF 2005.0 (based on the internal consistency of the contributing candidates) was only 1.0 nT, the true error, due to errors of commission not including unmodelled sources in the Earth's crust and magnetosphere, is probably closer to 5 nT. The error in IGRF-2010 is expected to be slightly larger (approximately 10 nT) because extrapolation of models from submission in October 2009 forward to 2010 was necessary (Lowes 2000). Regarding the predictive SV model, retrospective analysis of previous predictions has shown that errors of up to 20 nT yr−1 are likely (Maus et al. 2005b; Finlay et al. 2010). For further details on the limitations of the IGRF and difficulties in estimating its accuracy readers should consult the IGRF ‘health warning’ found at .

IGRF-11 Model Coefficients and Maps

In Table 2, the Schmidt semi-normalized spherical harmonic coefficients comprising IGRF-11 are listed. Note that IGRF-11 is a field model that spans the interval from 1900.0 to 2015.0; the entire set of MF coefficients at 5-yr intervals between 1900.0 and 2010.0 and predictive SV coefficients for 2010.0–2015.0 are given here to serve as a complete record of the model. Units are nT for the MF models and nT yr−1 for the predictive SV model. The coefficients are also available in various file formats at http://www.ngdc.noaa.gov/IAGA/vmod/igrf.html, along with software to compute the magnetic field components at times and locations of interest. IGRF-11 is also available from the world data centres listed in the Appendix.

Table 2

11th Generation International Geomagnetic Reference Field. Schmidt semi-normalized spherical harmonic coefficients are listed. Coefficients for degrees n = 1, 13 in units of nanotesla are listed for IGRF and definitive DGRF main field models. Coefficients for degrees n= 1,8 in units of nT yr−1 are listed for the predictive secular variation. Undefined coefficients are marked with ‘-’; these should be set to 0.0 in numerical calculations as in the electronic coefficient files available online at http://www.ngdc.noaa.gov/IAGA/vmod/igrf.html.

Table 2

11th Generation International Geomagnetic Reference Field. Schmidt semi-normalized spherical harmonic coefficients are listed. Coefficients for degrees n = 1, 13 in units of nanotesla are listed for IGRF and definitive DGRF main field models. Coefficients for degrees n= 1,8 in units of nT yr−1 are listed for the predictive secular variation. Undefined coefficients are marked with ‘-’; these should be set to 0.0 in numerical calculations as in the electronic coefficient files available online at http://www.ngdc.noaa.gov/IAGA/vmod/igrf.html.

Maps of the declination D, inclination I and total intensity F at Earth's surface in 2010 are displayed in Fig. 1. Together these quantities completely define the vector magnetic field. Recall that a purely dipolar field would possess two agonic lines (contours of zero D) running north–south, and a single dip equator (contour of zero I) displaced somewhat from the geographic equator. In contrast, the present geomagnetic field possesses a more complex morphology. It has three agonic lines; one that passes approximately north–south through the Americas, one that is located to the east of Asia and continues down through Indonesia and western Australia, and also one that passes down through central Europe extending as far south as Kenya before looping back northwards via India. Moreover, D is small over a large region spanning mid and low latitudes extending from northeastern Africa east to the Philippine islands. The map of I in the middle panel of Fig. 1 displays a distinctive deflection of the dip equator southwards at South America, an offset in the maximum of I from the geographic south pole towards Australia and also a tongue of high I extending westwards from Southern Africa. The map of F in 2010 in the bottom panel of Fig. 1 shows that the regions with highest field intensity are located in Siberia in the northern hemisphere and in the Southern Ocean and Antarctica southwards of Australia in the southern hemisphere. Perhaps the most striking feature of all is the low field intensity anomaly (compared to a dipole field) currently centred around Southern Brazil and Paraguay. This feature is often referred to as the South Atlantic Anomaly, and it is known to have important consequences regarding the impact of space weather on the near-Earth electromagnetic environment (Gledhill 1976; Heirtzler 2002; Facius & Reitz 2007).

Figure 1

Maps of the magnetic declination D (top, units are degrees), inclination I (middle, units are degrees) and total intensity F (bottom, units are nT) at the Earth's surface in 2010 from the new field model IGRF 2010.0. Molleweide projection is used, zero line is shown in green, positive contours in red and negative contours in blue.

Figure 1

Maps of the magnetic declination D (top, units are degrees), inclination I (middle, units are degrees) and total intensity F (bottom, units are nT) at the Earth's surface in 2010 from the new field model IGRF 2010.0. Molleweide projection is used, zero line is shown in green, positive contours in red and negative contours in blue.

All the features mentioned above are well-known from previous global field models; they have existed for at least several hundred years and have slowly evolved to their present configuration (Jackson et al. 2000). The current evolution of main field is illustrated in Fig. 2 which shows the IGRF-11 prediction of the average annual rate of change (SV) in the declination D, inclination I and total intensity F between 2010 and 2015. The predicted changes in D are small in the Pacific hemisphere, and consistent with the continuation of the long-established westward motion of field features in the Atlantic hemisphere. Changes in I are predicted to be largest at low latitudes, with the maximum negative change occurring near northeastern Brazil (close to where the dip equator is presently being deflected southwards) while the maximum positive change is predicted to occur close to Southern India. Considering the predicted changes in F, the largest decreases are predicted to the south of eastern North America as well as to the south west of South America. The later involves a continued deepening and westward motion of the South Atlantic Anomaly. The largest increases in F are predicted to take place in the equatorial part of the mid-Atlantic, in the southern Indian ocean (south-east of Africa), and in the region encompassing Iran, Kazakhstan, Afghanistan, Pakistan and India. Understanding of the future evolution of these field features requires detailed knowledge of the magnetohydrodynamic processes taking place in the liquid iron outer core. Such processes are only partly understood at present, but are the focus of much active research (see, for example, Olson 2007).

Figure 2

Maps of the predicted rate of change per year in the declination D (top, units are degrees yr−1), the inclination I (middle, units are degrees yr−1), and total intensity F (bottom, units are nT yr−1) at the Earth's surface for the interval 2010–2015 as predicted by IGRF-11. Molleweide projection is used, zero line is shown in green, positive contours in red and negative contours in blue.

Figure 2

Maps of the predicted rate of change per year in the declination D (top, units are degrees yr−1), the inclination I (middle, units are degrees yr−1), and total intensity F (bottom, units are nT yr−1) at the Earth's surface for the interval 2010–2015 as predicted by IGRF-11. Molleweide projection is used, zero line is shown in green, positive contours in red and negative contours in blue.

Further details concerning the evolution of the South Atlantic Anomaly since 1900 as captured by IGRF-11 are presented in Fig. 3 (see also Macmillan et al. 2009). The left plot shows how the lowest field intensity F within the South Atlantic Anomaly has systematically decreased since 1900. The decrease has been almost linear since 1940 (when the weakest intensity was 24 954 nT) until the present (the weakest intensity in 2010 was 22 590 nT) with an average decrease of 34 nT yr−1. There is no sign that the decrease of field intensity in the South Atlantic Anomaly is abating, with a further decrease to 22 430 nT predicted by 2015. The right hand plot documents the motion of the location of this point of lowest field intensity every 5 yr from 1900.0 to 2015.0, where the final point is a prediction. The position of lowest intensity has moved both southward and westward, but almost exclusively westwards since 1955. This analysis describes only the position with lowest intensity; the spatial extent of the south Atlantic anomaly has also increased during the past century, for example as measured by the area within the 28 000 nT contour of F. Note however, that the exact position of the lowest intensity point is known only rather crudely, particularly before 1960 when there was larger uncertainty in the field models.

Figure 3

Evolution of the South Atlantic Anomaly during the 20th century: Top plot (a) shows how the minimum F at the Earth's surface (in the South Atlantic Anomaly where the magnitude of the field is smallest) has decreased from 1900 towards the present day, units are nT. The bottom plot (b) tracks the location of the point of lowest field magnitude with time; the colour scale indicates the magnitude of F, with blue representing smallest magnitude, units are nT.

Figure 3

Evolution of the South Atlantic Anomaly during the 20th century: Top plot (a) shows how the minimum F at the Earth's surface (in the South Atlantic Anomaly where the magnitude of the field is smallest) has decreased from 1900 towards the present day, units are nT. The bottom plot (b) tracks the location of the point of lowest field magnitude with time; the colour scale indicates the magnitude of F, with blue representing smallest magnitude, units are nT.

In Fig. 4, we present the positions of the geomagnetic pole (as determined only from the n = 1 dipole field coefficients) and the magnetic dip pole (where inclination I is vertical, as determined from the entire field model to degree n=N) calculated from IGRF-11 and plotted as a function of time since 1900. Pole positions are also tabulated in Table 3. It is noteworthy that the North magnetic dip pole is currently moving at a high speed of over 50 km yr−1, as recently investigated by Newitt et al. (2009).

Figure 4

Motion of the magnetic dip pole (red) and geomagnetic pole (blue) since 1900 from IGRF-11 in the northern hemisphere (top) and the southern hemisphere (bottom). Stereographic projection is employed. The scale bar gives an indication of distance that is correct along lines of constant longitude and also along the middle lines of latitude shown.

Figure 4

Motion of the magnetic dip pole (red) and geomagnetic pole (blue) since 1900 from IGRF-11 in the northern hemisphere (top) and the southern hemisphere (bottom). Stereographic projection is employed. The scale bar gives an indication of distance that is correct along lines of constant longitude and also along the middle lines of latitude shown.

Table 3

Magnetic pole positions since et al. as determined from IGRF-11.

Table 3

Magnetic pole positions since et al. as determined from IGRF-11.

Because of the significant changes currently taking place in the internal geomagnetic field, including the development of the South Atlantic Anomaly and the motions of the geomagnetic poles described above, continued careful monitoring is essential. At the time of writing, the CHAMP and Ørsted satellites that were crucial sources of observations for IGRF-11 are approaching the end of their lifetimes, but fortunately one of the aims of the upcoming ESA Swarm mission (Friis-Christensen et al. 2006) is to provide the high-quality satellite data that will be of great importance to the next IGRF revision.

The 11th generation IGRF was computed from candidate models produced and evaluated by participating members of IAGA Working Group V-MOD who are listed as co-authors of this paper. Their institutes and the many organizations involved in operating the magnetic satellites CHAMP, Ørsted and SAC-C, observatories (see the appendix for a list), magnetic survey programmes, and the World Data Centres are thanked for their continued support of the IGRF project.

IGRF-11 Online Data Products

Further general information about the IGRF:

http://www.ngdc.noaa.gov/IAGA/vmod/igrf.html.

The coefficients of IGRF-11 in various file formats:

Fortran software for synthesizing the field from the coefficients: http://www.ngdc.noaa.gov/IAGA/vmod/igrf11.f

C software for synthesizing the field from the coefficients (Linux):http://www.ngdc.noaa.gov/IAGA/vmod/geomag70_linux.tar.gz

C software for synthesizing the field from the coefficients (Windows):http://www.ngdc.noaa.gov/IAGA/vmod/geomag70_windows.zip

Online computation of field components from the IGRF-11 model:http://www.ngdc.noaa.gov/geomagmodels/IGRFWMM.jsp

http://www.geomag.bgs.ac.uk/gifs/igrf_form.shtml

http://wdc.kugi.kyoto-u.ac.jp/igrf/point/index.html

Archive of legacy versions of the IGRF model:

Candidate models contributing to IGRF-11, and various test models are available for evaluation purposes:

http://www.ngdc.noaa.gov/IAGA/vmod/candidatemodels.html

Acknowledgments

The CHAMP mission is sponsored by the Space Agency of the German Aerospace Centre (DLR) through funds of the Federal Ministry of Economics and Technology, following a decision of the German Federal Parliament (grant code 50EE0944). Data retrieval and operation of the CHAMP satellite by the German Space Operations Centre (GSOC) is acknowledged. The Ørsted Project was made possible by extensive support from the Danish Government, NASA, ESA, CNES, DARA and the Thomas B. Thriges Foundation. The SAC-C mission was supported by CONAE together with NASA and DMI/DTU Space. The institutes that support magnetic observatories together with INTERMAGNET are thanked for promoting high standards of observatory practice. This is IPGP contribution no. 300(1). W.K., A.T. and Z.W. were funded by NASA and the NSF. The IGRF-11 task force finally wishes to express their gratitude to C. Manoj for maintaining the IGRF web pages at NGDC.

Appendix

World Data Centres WORLD DATA CENTRE FOR GEOPHYSICS AND MARINE GEOLOGY, BOULDER National Geophysical Data Center E/GC 325 Broadway Boulder, Colorado USA 80305-3328 TEL: +01 303 497 6826 FAX: +01 303 497 6513 EMAIL: ngdc.info@noaa.gov INTERNET: http://www.ngdc.noaa.gov/geomag/wdc/index.html

WORLD DATA CENTRE FOR GEOMAGNETISM, COPENHAGEN DTU Space, Juliane Maries vej 30 DK-2100, Copenhagen DENMARK TEL: +45 3532 5700 FAX: +45 353 62475 EMAIL: jrgm@space.dtu.dk INTERNET: http://www.space.dtu.dk/English/Research/Scientific_data_and_models

WORLD DATA CENTRE FOR GEOMAGNETISM, EDINBURGH British Geological Survey Murchison House, West Mains Road Edinburgh, EH9 3LA UNITED KINGDOM TEL: +44 131 650 0234 FAX: +44 131 668 4368 EMAIL: wdcgeomag@bgs.ac.uk INTERNET: http://www.wdc.bgs.ac.uk/catalog/master.html

WORLD DATA CENTRE FOR GEOMAGNETISM, KYOTO Data Analysis Center for Geomagnetism and Space Magnetism Graduate School of Science, Kyoto University Kitashirakawa-Oiwake Cho, Sakyo-ku Kyoto, 606-8502, JAPAN TEL: +81 75 753 3929 FAX: +81 75 722 7884 EMAIL: iyemori@kugi.kyoto-u.ac.jp INTERNET: http://wdc.kugi.kyoto-u.ac.jp

WORLD DATA CENTRE FOR GEOMAGNETISM, MUMBAI Indian Institute of Geomagnetism Colaba, Mumbai, 400 005, INDIA TEL: +91 22 215 0293 FAX: +91 22 218 9568 EMAIL: abh@iigs.iigm.res.in INTERNET: http://iigm.res.in

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Author notes

*
Member of IGRF-11 Task Force.