During recent decades the most important sources of vector magnetic field data for modeling the Earth’s main magnetic field were dedicated satellites designed for the magnetic surveys (MAGSAT, CHAMP, and Swarm missions). Now Swarm project (Friis-Christensen et al. 2006) provides the scientific community with a uniform data set for the entire IGRF 2015–2020 modeling period that allows us to derive candidate model based only on Swarm data.

The most common way to describe the spatial distribution of the Earth's main magnetic field is to fit the observed magnetic field with a set of spherical harmonics (Barton 1997). The general approach to deriving global models of the Earth’s magnetic field is well-known for a long time (Chapman and Bartels 1940), and we will skip its detailed overview here. An extended list of references is given in Alken et al. (2020, in press).

However, there are several problems that should be taken into account when building a model and it can be done in various ways.

The method of calculating the spherical harmonic coefficients allows us to separate the sources of the magnetic field lying inside and outside the surface on which the magnetic field is measured by a satellite. The ionospheric currents are external sources of the Earth's total magnetic field. But they are located inside the orbits of satellite and are included in the spherical harmonic coefficients describing the internal part of the Earth’s magnetic field.

During quiet geomagnetic conditions when currents induced in conducting Earth are small, the external sources of the magnetic field (such as magnetopause, ring, and field-aligned currents), should not theoretically affect the coefficients of the internal part, but they would be completely excluded if we had simultaneous measurements on the entire surface or they were constant during the whole period of data collection. In reality, to get as uniform coverage of the entire surface as possible, data for several days are required and external sources may change during this time and perfect separation is not possible.

Usually, to find spherical harmonic coefficients, the method of minimizing the difference between measured magnetic field values and calculated (modeled) values is used. If the surface around the Earth where magnetic field measurements were carried out is unevenly covered by measurement points, the method results in a better fit of the data in areas where the density of these points is greater, and it results in a worse fit in areas where there are fewer points. This is especially evident for data from the high-latitude and polar orbit satellites when there are significantly more measurements per unit of surface area at the high latitudes compared to the low latitudes. Usually, such latitudinal uneven distribution is taken into account by introducing weight coefficients proportional to the cosine of latitude into the minimization equation.