CHAOS-a model of the Earth's magnetic field derived from CHAMP, Orsted, and SAC-C magnetic satellite data

We have derived a model of the near-Earth magnetic field (up to spherical harmonic degree n= 50 for the static field, and up to n = 18 for the first time derivative) using more than 6.5 yr of high-precision geomagnetic measurements from the three satellites Orsted, CHAMP and SAC-C taken between 1999 March and 2005 December. Our modelling approach goes in several aspects beyond that used for recent models: (i) we use different data selection criteria and allow for higher geomagnetic activity (index Kp <= 2o), thus we include more data than previous models; (ii) we describe the temporal variation of the core field by splines (for n <= 14); (iii) we take magnetometer vector data in the instrument frame and co-estimate the Euler angles that describe the transformation from the magnetometer frame to the star imager frame, avoiding the inconsistency of using vector data that have been aligned using a different (pre-existing) field model; (iv) we account for the bending of the CHAMP optical bench connecting magnetometer and star imager by estimating Euler angles in 10 day segments and (v) we co-estimate degree-1 external fields separately for every 12 hr interval. The model provides a reliable representation of the static (core and crustal) field up to spherical harmonic degree n = 40, and of the first time derivative up to n = 15.