Intensity based predictions of the dipole field and their value in characterizing the Earth-like nature of models

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 work), the skill is high, and if the field decreases quickly, the skill is low. Applying threshold based predictions to Virtual Axial Dipole Moment (VADM) paleomagnetic records (PADM2M and Sint-2000) covering the last two million years, reveals a moderate skill of threshold-based predictions for Earth's dynamo. We note that the skill of threshold-based predictions on numerical dynamos is a fairly discriminating way of testing the Earth-like nature of the axial dipole field behavior of a model. This skill appears to be distinct from other criteria often used to characterize the Earth's dipole field behavior, such as its frequency content, the frequency with which reversals occur, or the relative time spent in transitional periods.