Long-term geomagnetic field variations inferred from geodynamo simulations

The long-term spatial and temporal behaviour of the geomagnetic field is largely unknown owing to a lack of data prior to 10~kyr ago. This raises important questions relating to the stability of the geodynamo process that generates the field: is the present field representative of the past field, does a time-averaged field (a field that does not change with further averaging) exist, and how long an averaging time is needed to find such a field if it exists. We investigate these issues using numerical geodynamo simulations. Simulations are selected by first analysing the agreement between morphological properties of synthetic and observed fields using the criteria of a previous study. A further criterion is then introduced to evaluate long-term temporal variations requiring that observed and synthetic axial dipole moment spectra can be fit by the same power law model to within the errors of the observations. In almost all simulations considered we find that periods of good morphological agreement between synthetic and observed field are shorter than periods of poor agreement, suggesting that the modern geomagnetic field is different to the past field. We find that the length of time needed to obtain a converged estimate of the time-averaged field is at least 400 kyr. Long term field variations are due almost entirely to the axial dipole while nonzonal components converge to their long-term average values on relatively short timescales. The time-averaged power spectrum is characterised by a zigzag pattern in all simulations, with high power in odd harmonic degrees and low power in even degrees, and this pattern emerges after as little as 15-20~kyr of averaging. Our results suggest that long-term characteristics of the field may emerge after relatively short averaging times, possibly within reach of the next generation of global geomagnetic field models.