COV-OBS.x2: 180 years of geomagnetic field evolution from ground-based and satellite observations

We present the geomagnetic field model COV-OBS.x2 that covers the period 1840-2020. It is primarily constrained by observatory series, satellite data, plus older surveys. Over the past two decades, we consider annual differences of 4-monthly means at ground-based stations (since 1996), and virtual observatory series derived from magnetic data of the satellite missions CHAMP (over 2001-2010) and Swarm (since 2013). A priori information is needed to complement the constraints carried by geomagnetic records and solve the ill-posed geomagnetic inverse problem. We use for this purpose temporal cross-covariances associated with auto-regressive stochastic processes of order 2, whose parameters are chosen so as to mimic the temporal power spectral density observed in paleomagnetic and observatory series. We aim this way to obtain as far as possible realistic posterior model uncertainties. These can be used to infer for instance the core dynamics through data assimilation algorithms, or an envelope for short-term magnetic field forecasts. We show that because of the projection onto splines, one needs to inflate the formal model error variances at the most recent epochs, in order to account for unmodeled high frequency core field changes. As a by-product of the core field model, we co-estimate the external magnetospheric dipole evolution on periods longer than 2 years. It is efficiently summarized as the sum of a damped oscillator (of period 10.5 years and decay rate 55 years), plus a short-memory (6 years) damped random walk.