Defining spatial uncertainty in main field magnetic models

Models of the Earth’s main magnetic field, such as the International Geomagnetic Reference Field (IGRF), are described by spherical harmonic (Gauss) coefficients to degree and order 13, which allows the continuous evaluation of the field at any location and time on or above the surface. They are created from satellite and ground-based magnetometer data and describe the large-scale variation (spatial scale of 3000 km) of the magnetic field in space and time under quiet conditions.

In its technical form, the model is a spectral representation and thus its formal uncertainty (as a wavelength) is of limited advantage to the spatial value expected by the average user.  To address this, we estimated the large-scale time-invariant spatial uncertainty of the IGRF based on the globally averaged misfit of the model to ground-based measurements at repeat stations and observatories between 1980 and 2021. As an example, we find the 68.3% confidence interval is 87 nT in the North (X) component, 73 nT in the East (Y) component and 114 nT in vertical (Z) component. These values represent an uncertainty of around 1 part in 500 for the total component which, for the (average) compass user is well below instrumental detectability.

For advanced users, in applications such as directional drilling, higher resolution models (<30 km) are required and the associated uncertainties are thus further divided into random and global as well as correlated and uncorrelated parts. However, the distribution of errors is Laplacian not Gaussian and communicating the subtleties of long-tailed distributions to end-users is often a difficult task. We describe the different types of uncertainties for magnetic field models and how these are used (or not) in industrial applications.