Coarse predictions of dipole reversals by low-dimensional modeling and data assimilation

Low-dimensional models for Earth's magnetic dipole may be a powerful tool for studying large-scale dipole dynamics over geological time scales, where direct numerical simulation remains challenging. We investigate the utility of several low-dimensional models by calibrating them against the signed relative paleointensity over the past 2 million years. Model calibrations are done by “data assimilation” which allows us to incorporate nonlinearity and uncertainty into the computations. We find that the data assimilation is successful, in the sense that a relative error is below 8% for all models and data sets we consider. The successful assimilation of paleomagnetic data into low-dimensional models suggests that, on millennium time scales, the occurrence of dipole reversals mainly depends on the large-scale behavior of the dipole field, and is rather independent of the detailed morphology of the field. This, in turn, suggests that large-scale dynamics of the dipole may be predictable for much longer periods than the detailed morphology of the field, which is predictable for about one century. We explore these ideas and introduce a concept of “coarse predictions”, along with a sound numerical framework for computing them, and a series of tests that can be applied to assess their quality. Our predictions make use of low-dimensional models and assimilation of paleomagnetic data and, therefore, rely on the assumption that currently available paleomagnetic data are sufficiently accurate, in particular with respect to the timing of reversals, to allow for coarse predictions of reversals. Under this assumption, we conclude that coarse predictions of dipole reversals are within reach. Specifically, using low-dimensional models and data assimilation enables us to reliably predict a time-window of 4 kyr during which a reversal will occur, without being precise about the timing of the reversal. Indeed, our results lead us to forecast that no reversal of the Earth's magnetic field is to be expected within the next few millennia. Moreover, we confirm that the precise timing of reversals is difficult to predict, and that reversal predictions based on intensity thresholds are unreliable, which highlights the value of our model based coarse predictions.