World Magnetic Model (WMM)
The World Magnetic Model (WMM) is a standard model of the core and large-scale crustal magnetic field. It is used extensively for navigation and in attitude and heading referencing systems by the UK Ministry of Defence, the US Department of Defense, the North Atlantic Treaty Organization and the International Hydrographic Organization. It is also used widely in civilian navigation and heading systems.
Irregular changes in the Earth’s core field limit the lifetime of any predictive model such as the WMM. For this reason a revision (WMM2010) was released in December 2009, valid until 2015. This model was produced by BGS jointly with the US National Geophysical Data Center (NGDC), with funding from the Defence Geographic Centre in the UK and the US National Geospatial-Intelligence Agency.
WMM2010 consists of a degree 12 spherical harmonic model of the Earth’s main field (MF) at 2010.0 produced by NGDC and a mean rate of change estimate (called secular variation, SV) over the period 2010.0 to 2015.0 produced by BGS.
In order to construct a SV model we wanted data with as much coverage in space and time as possible. We therefore used data from the CHAMP and Ørsted magnetic survey satellites spanning 1999 to 2009, at a 20 second sampling interval.
The WMM is a model of the core and large-scale crustal fields only. However the satellite data contain unwanted signals such as small-scale crustal, external ionospheric and magnetospheric and their induced counterparts. These fields would have added noise to the WMM2010 SV model and could have biased its estimates.
BGS employed two techniques to avoid the contamination caused by external magnetic fields. Firstly we rejected those data most contaminated by these sources, as identified by a combination of local time, geomagnetic indices and solar wind data. However, this had an unwanted side effect in leaving temporal gaps in the data. This would have had a detrimental effect on the quality of the SV estimates. We lessened this effect by including similarly selected data from 152 land-based observatories which have more continuous temporal coverage.
Our second technique was to initially model the larger unwanted sources that we could not easily reject. We therefore constructed what we called a ‘parent model’ for the WMM, including these extra sources, before removing the unwanted components to finalise the WMM. For example, our parent model extended to spherical harmonic degree 60 - a minimum wavelength in the magnetic field of around 660 km - to capture smaller scale crustal features. The WMM parent model also included harmonic terms for large-scale magnetospheric field variations and their induced components.
