Working Group V-MOD: Geomagnetic Field Modelling
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The International Geomagnetic Reference Field: A "Health" Warning
Revised, January 2010

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 5-yearly intervals, the latest being the 11th generation, produced and released by IAGA Working Group V-MOD (formerly V-8) 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.

INTRODUCTION

The 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 time-scale of months and longer, in an as yet unpredictable manner. This so-called 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 easily-usable 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 V-8/V-MOD 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 1979-1980 (MAGSAT), and from 1999 (Ørsted, CHAMP). For other times our knowledge is significantly poorer because of the poorly-known 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 order-of-magnitude working approximations. (The different figures arise because of the different data and methods of analysis used at different times for different epochs.)

Table 1

  • For the IGRF models for 1900-1940, the modelers estimated an accuracy of about 50 nT rms. Experience indicates, however, that such estimates are usually too small, and I suggest using 100 nT rms.
  • For the DGRFs for epochs 1945-1960 I suggest rms errors decreasing linearly from about 300 nT in 1945 to about 100 nT in 1960.
  • For the DGRFs from1965 to 1995 (other than 1980) I think that a reasonable approximation is that the rms error is about 50 nT.
  • For the 1980 DGRF, different estimates of the accuracy of the coefficients on which it was based lead to uncertainties in the global rms vector in the range 1-10 nT. Because the DGRF coefficients were rounded to 1 nT (see below), a reasonable working approximation would be an overall uncertainty of about 10 nT rms.
  • For the DGRFs from 2000 onwards satellite data were again available, and analysis techniques steadily improved. For the 2000 DGRF I suggest an overall uncertainty of about 10 nT rms, and 5 nT rms for the 2005 DGRF.
  • The production of the IGRF for the current epoch inevitably involves forward extrapolation of the observational data, and if there has not been a recent satellite survey the data themselves may well be inadequate. So the IGRF yyyy for the current epoch will inevitably be less accurate than the retrospective models; I suggest using 10 nT rms while we have satellite data.
  • The accompanying predictive secular variation is an estimate of the average rate of change to be expected over the next 5 years. Unfortunately the real SV is liable to unpredictable change. Past experience has shown that over the 5-year extrapolation period the predictive SV is typically wrong by about 20 nT/year. Note that this implies significantly increasing the uncertainty of the main-field model for dates after the epoch of the last IGRF model.
  • Secular 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

    1. When the IGRF was started in 1968 the errors were large, and it was sufficiently accurate to specify the coefficients to the nearest nT. This approximation added about 9 nT rms error to the resultant field magnitude, but it has had no significant effect, except for times very near 1980.0. For epochs from 2000 the rounding was to 0.1 nT, and will have no effect on the uncertainties on the uncertainties of IGRF (prospective) models . For epochs from 2005, the rounding is to 0.01 nT for the DGRF models. This change was needed because for harmonic degrees higher than about 6 the accuracy of the coefficients was better than the error associated with rounding to 0.1 nT. (The variation with degree is because we are using semi-normalized associated Legendre polynomials.) But note that for all the coefficients, rounding to 0.01 nT greatly overestimates their accuracy.
    2. All independent sources of error add as their mean square, even though they are quoted here as root mean square.
    3. At any one place, a 10 nT vector error could be 10 nT in any one of the three (X, Y, or Z) orthogonal components, or be shared among them. A 10 nT global rms vector error corresponds to global rms values of about 5, 5, and 7 nT for X, Y, and Z respectively. But remember that at some places on the surface there will be errors several times larger than the rms value. And errors will often be particularly large in regions where there is not much data, such as the south Pacific!
    4. Similarly, a given vector error might appear as an error in either total intensity F, inclination I, or declination D, or be shared between them. A 10 nT vector rms local error gives rms values of about 5-7 nT in F (going from geomagnetic equator to pole), 0.8-0.3 arcminute in I (equator to pole), and 0.6-1.2 arcminute in D (from the equator to about 60 degree geomagnetic latitude; much more nearer the poles).
    5. For global rms values other than 10 nT, all the above values change proportionately.

    THE IGRF AS A MODEL OF THE FIELD FROM THE EARTH'S CORE

    The 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 200-300 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 5-10 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 shorter-wavelength field, including that from the core, is ignored by the model. Again, this core-field contribution is not separable from the crustal field, but not unreasonable extrapolations suggest that about 35 nT rms of short-wavelength 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 FIELD

    If 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, small-scale, field, typically of magnitude 200 nT, but often much larger.

    There are also a large variety of time-varying fields, both man-made (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 large-scale 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
    Author, IAGA Working Group VMOD


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    URL: http://www.ngdc.noaa.gov/IAGA/vmod/igrfhw.html
    Revised: 1 January 2010



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