Modelling the archaeomagnetic field under spatial constraints from dynamo simulations: a resolution analysis

Archaeomagnetic observations are key to recovering the behaviour of the geomagnetic field over the past few millennia. The corresponding data set presents a highly heterogeneous distribution in both space and time. Furthermore, the data are affected by substantial age and experimental uncertainties. In order to mitigate these detrimental properties, time-dependent global archaeomagnetic field models are usually constructed under spatial and temporal regularization constraints, with the use of bootstrap techniques to account for data uncertainties. The models so obtained are the product of an adjustable trade-off between goodness-of-fit and model complexity. The spatial complexity is penalized by means of a norm reflecting the minimization of Ohmic dissipation within the core. We propose in this study to resort to alternative spatial constraints relying on the statistics of a numerical dynamo simulation with Earth-like features. To that end, we introduce a dynamo norm in an ensemble least-squares iterative framework, the goal of which is to produce single-epoch models of the archaeomagnetic field. We first validate this approach using synthetic data. We next construct a redistributed archaeomagnetic data set between 1200 BC and 2000 AD by binning the data in windows of 40-yr width. Since the dynamo norm is not adjustable, we can legitimately calculate a resolution matrix to quantify the resolving power of the available archaeomagnetic data set. Gauss coefficients are resolved up to spherical harmonic degree 3 for the first thousand years of the interval, to degree 4 for the next thousand years and to degree 5 during the last millennium. These conclusions are based on the distribution and uncertainties that characterize the data set, and do not take into account the possible presence of outliers. Comparison between our model, called AmR, and previously published archaeomagnetic field models confirms the archaeomagnetic resolution analysis: it highlights the dichotomy between data-driven coefficients for which model predictions coincide (within their respective uncertainties), and prior-driven coefficients. This study opens the way to physics-based models of the archaeomagnetic field; future work will be devoted to integrating the framework here introduced into a time-dependent ensemble assimilation scheme.