Understanding and Predicting Geomagnetic Dipole Reversals Via Low Dimensional Models and Data Assimilation

Abstract:

We investigate the geophysical relevance of low-dimensional models of the geomagnetic dipole field
by comparing these models to the signed relative paleomagnetic intensity over the past 2 Myr.
The comparison is done via Bayesian statistics, implemented numerically by Monte Carlo (MC) sampling.
We consider several MC schemes, as well as two data sets to show the robustness of our approach
with respect to its numerical implementation and to the details of how the data are collected.
The data we consider are the Sint-2000 [1] and PADM2M [2] data sets.
We consider three stochastic differential equation (SDE) models and one deterministic model.

Experiments with synthetic data show that it is feasible that a low dimensional model
can learn the geophysical state from data of only the dipole field,
and reveal the limitations of the low-dimensional models.
For example, the G12 model [3]
(a deterministic model that generates dipole reversals by crisis induced intermittency)
can only match either one of the two important time scales we find in the data.

The MC sampling approach also allows us
to use the models to make predictions of the dipole field.
We assess how reliably dipole reversals can be predicted
with our approach by hind-casting five reversals documented over the past 2 Myr.
We find that, besides its limitations, G12 can be used to predict reversals reliably,
however only with short lead times and over short horizons.
The scalar SDE models on the other hand are not useful for prediction of dipole reversals.

References

Valet, J.P., Maynadier,L and Guyodo, Y., 2005, Geomagnetic field strength and reversal rate over the past 2 Million years, Nature, 435, 802-805.

Ziegler, L.B., Constable, C.G., Johnson, C.L. and Tauxe, L., 2011, PADM2M: a penalized maximum likelihood model of the 0-2 Ma paleomagnetic axial dipole moment, Geophysical Journal International, 184, 1069-1089.

Gissinger, C., 2012, A new deterministic model for chaotic reversals, European Physical Journal B, 85:137.