The magnetic field of the Earth is composed of many sources. Isolating them from direct measurements at the Earth's surface or at the altitude of low orbiting satellites is a challenging task. Nevertheless, advantage can be taken from the distinct dynamics of these sources. Whereas internal fields such as the core field or the lithospheric field are either evolving slowly (the core field) or are almost static (the lithospheric field), external fields such as the ionospheric field, the magnetospheric field or the fields the latter induce within the upper mantle, the crust and the ocean, vary extremely rapidly in time. In general, magnetic field models deriving from ground-based observatory and satellite data, are a priori enforcing these specific temporal properties, but they often neglect the crucial information coming from the particular morphologies and spatial correlations that each field is exhibiting. Yet, combining spatial and temporal constraints within an inversion framework would improve the separation of the different contributions to the observed magnetic field. Nevertheless, a high model complexity necessarily implies important computational needs. Moreover, to obtain an optimal separation, every overlapping field have to be simultaneously considered, and this, down to their smallest significant timescales, which in turn leads to a further escalation in numerical costs. This is why we propose to develop a sequential data assimilation tool referred as the Kalman filter algorithm, in order to combine sophisticated spatio-temporal models for the different magnetic field sources and measurements from ground based observatories and satellites, sampled at a highly rate. This method is not only attractive because it drastically reduces the needs in computational power, it also gives access to uncertainties estimates and predictions of future states. In a first step, the dynamical models for the different fields will be of the autoregressive type. Characterizing these stochastic processes with scale dependent parameters, will allow us to simulate complex space time dynamics. Furthermore, since these processes are Gaussian, they can be incorporated in the linear version of the Kalman filter, making the algorithm extremely efficient and statistically accurate. In a second step, physical models such as a three dimensional numerical simulation of the geodynamo, or a model simulating magnetic induction occurring within the oceans, will be incorporated into the algorithm and combined to the stochastic models. With this project we will construct a magnetic field model of unprecedented spatial and temporal resolution, covering the entire 20th century and extending to today. It will exploit the full potential of the available magnetic field data set, drawing upon information from ground based observatory measurements up to the high precision data emanating from the Swarm constellation.

You can access the model for the geomagnetic field calculated with the new approach on https://ionocovar.agnld.uni-potsdam.de/Kalmag/.