Summary We study predictions of reversals of Earth’s axial magnetic dipole field that are based solely on the dipole’s intensity. The prediction strategy is, roughly, that once the dipole intensity drops below a threshold, then the field will continue to decrease and a reversal (or a major excursion) will occur. We first present a rigorous definition of an intensity threshold-based prediction strategy and then describe a mathematical and numerical framework to investigate its validity and robustness in view of the data being limited. We apply threshold-based predictions to a hierarchy of numerical models, ranging from simple scalar models to 3D geodynamos. We find that the skill of threshold-based predictions varies across the model hierarchy. The differences in skill can be explained by differences in how reversals occur: if the field decreases towards a reversal slowly (in a sense made precise in this paper), the skill is high, and if the field decreases quickly, the skill is low. Such a property could be used as an additional criterion to identify which models qualify as Earth-like. Applying threshold-based predictions to Virtual Axial Dipole Moment (VADM) paleomagnetic reconstructions (PADM2M and Sint-2000) covering the last two million years, reveals a moderate skill of threshold-based predictions for Earth’s dynamo. Besides all of their limitations, threshold-based predictions suggests that no reversal is to be expected within the next 10 kyr. Most importantly, however, we show that considering an intensity threshold for identifying upcoming reversals is intrinsically limited by the dynamic behavior of Earth’s magnetic field.

Summary Geomagnetic data assimilation merges past and present-day observations of the Earth’s magnetic field with numerical geodynamo models and the results are used to initialize forecasts. We present a new “proxy model” that can be used to test, or rapidly prototype, numerical techniques for geomagnetic data assimilation. The basic idea for constructing a proxy is to capture the conceptual difficulties one encounters when assimilating observations into high-resolution, 3D geodynamo simulations, but at a much lower computational cost. The framework of using proxy models as “gate-keepers” for numerical methods that could/should be considered for more extensive testing on operational models has proven useful in numerical weather prediction, where advances in data assimilation and, hence, improved forecast skill, are at least in part enabled by the common use of a wide range of proxy models. We also present a large set of systematic data assimilation experiments with the proxy to reveal the importance of localization and inflation in geomagnetic data assimilation.

Summary It is well known that the axial dipole part of Earth’s magnetic field reverses polarity, so that the magnetic north pole becomes the south pole and vice versa. The timing of reversals is well documented for the past 160 Myr, but the conditions that lead to a reversal are still not well understood. It is not known if there are reliable “precursors” of reversals (events that indicate that a reversal is upcoming) or what they might be. We investigate if machine learning (ML) techniques can reliably identify precursors of reversals based on time series of the axial magnetic dipole field. The basic idea is to train a classifier using segments of time series of the axial magnetic dipole. This training step requires modification of standard ML techniques to account for the fact that we are interested in rare events – a reversal is unusual, while a non-reversing field is the norm. Without our tweak, the ML classifiers lead to useless predictions. Perhaps even more importantly, the usable observational record is limited to 0-2 Ma and contains only five reversals, necessitating that we determine if the data are even sufficient to reliably train and validate an ML algorithm. To answer these questions we use several ML classifiers (linear/nonlinear support vector machines and long short-term memory networks), invoke a hierarchy of numerical models (from simplified models to 3-D geodynamo simulations), and two paleomagnetic reconstructions (PADM2M and Sint-2000). The performance of the ML classifiers varies across the models and the observational record and we provide evidence that this is not an artifact of the numerics, but rather reflects how “predictable” a model or observational record is. Studying models of Earth’s magnetic field via ML classifiers thus can help with identifying shortcomings or advantages of the various models. For Earth’s magnetic field, we conclude that the ability of ML to identify precursors of reversals is limited, largely due to the small amount and low frequency resolution of data, which makes training and subsequent validation nearly impossible. Put simply: the ML techniques we tried are not currently capable of reliably identifying an axial dipole moment (ADM) precursor for geomagnetic reversals. This does not necessarily imply that such a precursor does not exist, and improvements in temporal resolution and length of ADM records may well offer better prospects in the future.