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-year intervals, the latest being the 13th generation. IGRF is produced and released by IAGA Working Group V-MOD (formerly V-8). It has achieved worldwide acceptance as a standard and has proved valuable for many applications. However, **it can produce inaccurate results** when used incorrectly.

## 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 nanoteslas (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 on a time-scale of months and longer, in an 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 that vary with time.

The IGRF is intended to model the surface level effects of the part of Earth’s magnetic field that originates below the surface. At any one epoch, the IGRF specifies the numerical coefficients of a truncated spherical harmonic series. The model is truncated at n=10 with 120 coefficients up until the year 2000, but after 2000 the truncation is at n=13, with 195 coefficients. The model is specified every five years for epochs 1900.0, 1905.0 etc.

### 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 time periods with global coverage by satellites measuring the vector field. This occurred in 1979–1980 (MAGSAT), and from 1999 (Ørsted, CHAMP). For other time periods, our knowledge is limited because of the poorly-known time variation of the geomagnetic field.

Estimating the uncertainty of numerical models is difficult. The values in Table 1 are reasonable order-of-magnitude working approximations based on comparisons of older IGRF and definitive geomagnetic reference field (DGRF) models with later versions. The different figures arise because of the different data and methods of analysis used at different times for different epochs.

Time Period | Suggested Value |
---|---|

IGRFs: 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. |

DGRFs: 1945–1960 | The author suggests rms errors decreasing linearly from about 300 nT in 1945 to about 100 nT in 1960. |

DGRFs: 1965–1995 | A reasonable approximation is that the rms error is about 50 nT. |

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. |

DGRFs: 2000–Present | Satellite data became available again after 2000, and analysis techniques steadily improved. For the 2000 DGRF, the author suggests an overall an overall uncertainty of about 10 nT rms, and 5 nT rms for the 2005 DGRF. |

IGRF: Current Model |
The production of the IGRF for the current epoch involves forward extrapolation of the observational data, and if there has not been a recent satellite survey, then the data themselves may well be inadequate. So the IGRF yyyy for the current epoch will inevitably be less accurate than the retrospective models; It is suggested to use 10 nT rms when satellite data is available. The accompanying predictive secular variation is an estimate of the average rate of change to be expected during the next five years. However, the real SV is subject to unpredictable change. Past experience has shown that during 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. However, the use of linear interpolation over five years does not significantly increase the above rms errors for the main field until 2000, except for a few years around 1980. From 2000–present, linear interpolation might lead to increased errors at certain times.

Note that a stepwise linear sv is inherent in the IGRF model. This model of the sv is only intended for interpolating main field models; it is a very poor model of the actual instantaneous time rate of change of the geomagnetic main field.

### Miscellaneous Notes

- 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 resulting 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 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 six, the accuracy of the coefficients was better than the error associated with rounding to 0.1 nT. (The variation with degree is because scientists are using semi-normalized associated Legendre polynomials.) However, for all the coefficients, rounding to 0.01 nT greatly overestimates their accuracy.
- All independent error sources add as their mean square, even though they are quoted here as root mean square.
- At any specific location, 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. Some places on the surface there will be errors several times larger than the rms value. Errors will often be particularly large in regions where there is not much data, such as the south Pacific.
- 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).
- For global rms values other than 10 nT, all the above values change proportionately.

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 Earth's surface from this source, the observed core field is predominantly of long wavelength. A significant contribution also comes from the magnetized rocks of Earth's crust; this contribution is predominantly a much shorter wavelength, and typically amounts to 200–300 nT rms.

There is no way to separate the core field from the crustal field for a given wavelength. Although the crustal field is typically at a much shorter length scale than the core field, there is almost certainly a finite (essentially constant) contribution from the crust in the IGRF models (i.e. in harmonics at and below degree n=10). This contribution is not separably measurable, but reasonable 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. Because the contributions from core and crustal field wavelengths are indistinguishable, plausible 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.

If you measure the magnetic field at a point on Earth's surface, do not expect to get the value predicted by the IGRF.

Other error or variation sources include fixed contributions from buildings, parked cars, etc. The magnetization of crustal rocks can also add local, small-scale fields that are typically at a magnitude 200 nT. However, these fields can also be much larger.

There are also many man-made (traffic, electric trains, and trams, etc.) and natural (from electric currents in the ionosphere and magnetosphere) time-varying fields, and the associated induced fields from currents induced in the conducting Earth. The ionospheric and magnetospheric fields occur at time scales 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), and more than 1000 nT 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.