Secular variation prediction of the Earth’s magnetic field using core surface flows

Abstract

The Earth’s magnetic field is generated by fluid motion of liquid iron in the outer core. Flows at the top of the outer core are believed to be responsible for the secular variation (SV) observed at the surface of the Earth. Modelling of this flow is open to considerable ambiguity, though methods adopting different physical assumptions do lead to similar flow velocity regimes. Some aspects of the ambiguities are investigated in this thesis. The last decade has seen a significant improvement in the capability to observe the global field at high spatial resolution. Several satellite missions have been launched, providing a rich new set of scalar and vector magnetic measurements from which to model the global field in detail. These data complement the existing record of groundbased observatories, which have continuous temporal coverage at a single point. I exploit these new data to model the secular variation (SV) globally and attempt to improve the core flow models that have been constructed to date. Using the approach developed by Mandea and Olsen (2006) I create a set of evenly distributed ‘Virtual Observatories’ (VO), at 400km above the Earth’s surface, encompassing satellite measurements from the CHAMP satellite over seven years (2001-2007), inverting the SV calculated at each VO to infer flow along the core-mantle boundary. Direct comparison of the SV generated by the flow model to the SV at individual VO can be made. Thus, the residual differences can be investigated in detail. Comparisons of residuals from flow models generated from a number of VO datasets provide evidence that they are consistent with internal and external field effects in the satellite data. I also show that the binning and processing of the VO data can induce artefacts, including sectorial banding, into the residuals. By employing the core flows from the inversion of SV data it may be possible to forecast the change of the present magnetic field (as measured) forwards in time for a short time period (e.g. less than five years) within an acceptable error budget. Using simple advection of steady or non-steady flows to forecast magnetic field change gives reasonably good fit to field models such as GRIMM, POMME or xCHAOS (< 50nT root mean square difference after five years). The forecast of the magnetic field change can be improved by optimally assimilating measurements of the field into the forecast from flow models at discrete points in time (e.g. annually). To achieve this, an Ensemble Kalman Filter (EnKF) can be used to the capture non-linearity of the model and delineate the error bounds by means of a Monte Carlo representation of the field evolution over time. In the EnKF model, an ensemble of probable state vectors (Gauss coefficients) evolve over time, driven by SV derived from core flows. The SV is randomly perturbed at each step before addition to the state vectors. The mean of the ensemble is chosen as the most likely state (i.e. field model) and the error associated with the estimate can be gauged from the standard deviation from the mean. I show an implementation of the EnKF for steady and non-steady flows generated from ‘Virtual Observatory’ field models, compared to the field models GRIMM and xCHAOS over the period 2002–2008. Using the EnKF, the maximum difference never exceeds 25nT over the period. This promising approach allows measurements to be included into model predictions to improve the forecast.