Co-estimating geomagnetic field and calibration parameters: modeling Earth’s magnetic field with platform magnetometer data

Abstract

Models of the geomagnetic field rely on magnetic data of high spatial and temporal resolution to give an accurate picture of the Earth’s internal magnetic field and its time-dependence. The magnetic data from low-Earth orbit satellites of dedicated magnetic survey missions such as CHAMP and Swarm play a key role in the construction of such models. Unfortunately, there are no magnetic data available from such satellites after the end of the CHAMP mission in 2010 and before the launch of the Swarm mission in late 2013. This limits our ability to recover signals on timescales of 3 years and less during this gap period. The magnetic data from platform magnetometers carried by satellites for navigational purposes may help address this data gap provided that they are carefully calibrated. Earlier studies have demonstrated that platform magnetometer data can be calibrated using a fixed geomagnetic field model as reference. However, this approach can lead to biased calibration parameters. An alternative approach has been developed in the form of a co-estimation scheme which consists of simultaneously estimating both the calibration parameters and a model of the internal part of the geomagnetic field. Here, we go further and develop a scheme, based on the CHAOS field modeling framework, that involves co-estimation of both internal and external geomagnetic field models along with calibration parameters of platform magnetometer data. Using our implementation, we are able to derive a geomagnetic field model spanning 2008 to 2018 with satellite magnetic data from CHAMP, Swarm, secular variation data from ground observatories, and platform magnetometer data from CryoSat-2 and the GRACE satellite pair. Through a number of experiments, we explore correlations between the estimates of the geomagnetic field and the calibration parameters, and suggest how these may be avoided. We find evidence that platform magnetometer data provide additional information on the secular acceleration, especially in the Pacific during the gap between CHAMP and Swarm. This study adds to the evidence that it is beneficial to use platform magnetometer data in geomagnetic field modeling.

Applications for CryoSat-2 satellite magnetic data in studies of Earth’s core field variations

“…An undesirable consequence is that, for the higher harmonics, the first time derivative effectively becomes a time average over an increasingly long interval, rather than an estimate of the instantaneous secular variation (Olsen et al 2009). CryoSat-2 data has already been used in the construction of such time-dependent spherical harmonic field models by Alken et al (2020a), Finlay et al (2020) and Kloss et al (2021). From the viewpoint of accessing more detailed information on the spatial and temporal structure of the field, it is also of interest to look at alternative techniques for studying secular variation that can complement the traditional SH approach.…”

Magnetometer data from the GRACE satellite duo

“…We hope that the scientific community will find GRACE magnetic data useful for scientific studies, both regarding sources in Earth's interior and space physics/ space weather applications. One example of research that used (a preliminary version of the) GRACE magnetic data is the geomagnetic field modelling study by Kloss et al (2021), who jointly analysed magnetic data from the satellites Ørsted, CHAMP, CryoSat-2, GRACE and Swarm. Fig.…”

“…This makes GRACE magnetic data along with similar platform magnetometer data from the CryoSat-2 satellite interesting for modelling Earth's core field, as shown, e.g. by Kloss et al (2021).…”

“…Alternatively, a geomagnetic field model can be co-estimated with (at least some of ) the magnetometer calibration instead of using an a priori field model. Alken et al (2020) and Kloss et al (2021) describe such an approach, and Kloss et al (2021) applied it to GRACE magnetic data after correcting for spacecraft disturbance fields and magnetometer non-linearities using (a preliminary version of ) the "common" calibration parameters determined in the present paper.…”

Special issue “Characterization of the geomagnetic field and its dynamic environment using data from space-based magnetometers”

“…1). Kloss et al (2021) present a similar approach, go further, and co-estimate both the internal (core) and the external (magnetospheric) part of geomagnetic field models along with magnetometer calibration parameters. By that, they derive a geomagnetic field model spanning 2008 to 2018 with satellite magnetic data from CHAMP, Swarm, data from ground observatories, and platform magnetometer data from CryoSat-2 and the GRACE satellite pair.…”