The International Geomagnetic Reference Field: A "Health" Warning
 
Key words: IGRF, uses and limitations, health warning, geomagnetic reference field, geomagnetic field model, secular variation 

The International Geomagnetic Reference Field (IGRF) was introduced by the International Association of Geomagnetism and Aeronomy (IAGA) in 1968 in response to the demand for a standard spherical harmonic representation of the Earth's main field. The model is updated at 5yearly intervals, the latest being the 11th generation, produced and released by IAGA Working Group VMOD (formerly V8) December 2009. The IGRF has achieved worldwide acceptability as a standard and has proved valuable for many applications, BUT INAPPROPRIATE USE COULD SERIOUSLY DAMAGE THE CREDIBILITY OF YOUR RESULTS ! This page attempts to indicate the limitations of the IGRF. INTRODUCTIONThe Earth's magnetic field crudely resembles that of a central dipole. On the Earth's surface the field varies from being horizontal and of magnitude about 30 000 nT near the equator to vertical and about 60 000 nT near the poles; the root mean square (rms) magnitude of the vector over the surface is about 45 000 nT. The internal geomagnetic field also varies in time, on a timescale of months and longer, in an as yet unpredictable manner. This socalled secular variation (SV) has a complicated spatial pattern, with a global rms magnitude of about 80 nT/year. Consequently, any numerical model of the geomagnetic field has to have coefficients which vary with time. The International Geomagnetic Reference Field is an attempt by IAGA to provide an easilyusable model acceptable to a variety of users. It is meant to give a reasonable approximation, near and above the Earth's surface, to that part of the Earth's magnetic field which has its origin inside the surface. At any one epoch, the IGRF specifies the numerical coefficients of a truncated spherical harmonic series: for dates until 2000 the truncation is at n=10, with 120 coefficients, but from 2000 the truncation is at n=13, with 195 coefficients. Such a model is specified every 5 years, for epochs 1900.0, 1905.0 etc. For dates between the model epochs, coefficient values are given by linear interpolation. For the 5 years after the most recent epoch there is a linear secular variation model for forward extrapolation; this SV model is truncated at n=8, so has 80 coefficients  in effect the next 40 or 115 coefficients are defined to be zero. When using models, to avoid ambiguity you should state explicitly which IGRF Generation you are using; the error estimates in the following discussion refers to the set of models of the 11th Generation. For simplicity in this discussiom, the model for the current epoch, and those for some earlier epochs, is designated by "IGRF" followed by the epoch, e.g. IGRF2010. At some later time these IGRF yyyy models are replaced by definitive DGRF yyyy models; note that while the D stands for Definitive, this is in the sense that Working Group V8/VMOD thought (rightly or wrongly) that it would not be able to do significantly better in the future, NOT that the values are exact! When working retrospectively, interpolate between the appropriate DGRF yyyy models if they exist; for current work, and if there is not a DGRF model, then use the appropriate IGRF model. In any case ALWAYS specify exactly what model has been used, so that later, when a DGRF has been produced, the necessary corrections can be made to your data and results. The IGRF is inevitably an imperfect model. Firstly, the numerical coefficients provided will not be correct: the model field produced will differ from the actual field we are trying to model  "errors of commission". Secondly, because of the truncation, the IGRF models represent only the lower spatial frequencies (longer wavelengths) of the field: higher spatial frequency components of the field are not accounted for in our model  "errors of omission". Thirdly, there are also other contributions to the observed field that the IGRF is NOT trying to model. These three aspects are now discussed in more detail. 

ERRORS OF COMMISSION (due to errors in the numerical coefficients)Geomagnetic main field Errors in the coefficients lead to errors in the resulting model field, which are most easily summarized as a root mean square vector error in the field when averaged over the Earth's surface. Because of the time variation of the field, really good models can only be produced for times when there is global coverage by satellites measuring the vector field. This occurred in 19791980 (MAGSAT), and from 1999 (Ørsted, CHAMP). For other times our knowledge is significantly poorer because of the poorlyknown time variation of the geomagnetic field. Estimating the uncertainty of numerical models is notoriously difficult. Mainly by comparing some IGRF and DGRF models with ones produced later, I suggest the values shown in Table 1 as reasonable orderofmagnitude working approximations. (The different figures arise because of the different data and methods of analysis used at different times for different epochs.) Table 1Secular variation The geomagnetic field does not vary linearly with time but until 2000, except for a few years round 1980, the use of linear interpolation over 5 years does not significantly increase the above rms errors for the main field. From 2000, linear interpolation might lead to increased errors at certain times. Note that a stepwise linear secular variation is inherent in the IGRF model. This model of the secular variation is intended ONLY for use in interpolating main field models; it will be a VERY POOR model of the actual instantaneous time rate of change of the geomagnetic main field. Miscellaneous notes


THE IGRF AS A MODEL OF THE FIELD FROM THE EARTH'S COREThe field observed near the surface (typically 45 000 nT) comes predominantly from electric currents in the Earth's fluid core; because of the large distance of the Earth's surface from this source, the observed core field is predominantly of long wavelength. But a significant contribution also comes from the magnetized rocks of the Earth's crust; this contribution is predominantly of much shorter wavelength, and amounts typically to 200300 nT rms. For a given wavelength there is no way of separating the core field from the crustal field. Although the crustal field is mostly of much shorter length scale than the core field, there is almost certainly a finite (essentially constant) contribution from the crust present in the IGRF models (i.e. in harmonics at and below degree n=10). This contribution is not separably measurable, but not unreasonable models suggest its magnitude is about 510 nT global vector rms. Conversely, because the shortest (equatorial) wavelength which can be represented in an IGRF model truncated to n=10 is about 4000 km, any shorterwavelength field, including that from the core, is ignored by the model. Again, this corefield contribution is not separable from the crustal field, but not unreasonable extrapolations suggest that about 35 nT rms of shortwavelength core field is being ignored. From 2000 the truncation level was increased to n=13, probably reducing this to about 10 nT rms. OTHER CONTRIBUTIONS TO THE OBSERVED FIELDIf you measure the magnetic field at a point on the Earth's surface, do not expect to get the value predicted by the IGRF! Quite apart from the errors discussed above, there might be fixed contributions from buildings, parked cars, etc., and the magnetization of crustal rocks will certainly add its own local, smallscale, field, typically of magnitude 200 nT, but often much larger. There are also a large variety of timevarying fields, both manmade (traffic, DC electric trains and trams, etc.) and natural (from electric currents in the ionosphere and magnetosphere), and the associated induced fields from currents induced in the conducting earth. The ionospheric and magnetospheric fields occur at time scales mostly ranging from seconds to hours; in "quiet" conditions they may be as small as 20 nT (though enhanced near the geomagnetic equator and over the polar caps), but up to 1000 nT and more during a magnetic storm. On a longer time scale (days to years), the largescale magnetic field of the external ring current (approximately represented by the Dst index) will give perhaps 1000 nT during and after a magnetic storm. F.J. Lowes

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