In this paper we examine the core surface flow obtained by an inversion of a continuous model of the geomagnetic field and its temporal variation using the diffusion-less induction equation. The continuous CHAOS model is derived from satellite data up to spherical harmonic degree 14 and covers the period 1999 to 2006. The CHAOS secular variation, when downward continued to the core surface, shows stripe-like features, which can be attributed to spherical harmonic degree 12 and higher. These contributions are removed by applying a tapering method, and the resulting tapered model is then inverted for the core surface flow. Satellite-based field models have a high spatial resolution; however, their temporal resolution is limited. In order to enhance the temporal resolution of the flow, we additionally constrain the flow to fit the secular variation from ground-based observatory data.A range of solutions, subject to different constraints, are computed, two flow hypotheses being considered: purely toroidal flow and tangentially geostrophic flow.We show that both flow types provide similar results; however, the purely toroidal flow provides a better fit to the secular variation in the equatorial region than Finally, we compare observed changes in the length-of-day and the predictions from the flow solutions.

Two recent magnetic eld models, GRIMM and xCHAOS, describe core eld accelerations with similar behavior up to Spherical Harmonic (SH) degree 5, but which differ signi cantly for higher degrees. These discrepancies, due to different approaches in smoothing rapid time variations of the core eld, have strong implications for the interpretation of the secular variation. Furthermore, the amount of smoothing applied to the highest SH degrees is essentially the modeler's choice. We therefore investigate new ways of regularizing core magnetic eld models. Here we propose to constrain eld models to be consistent with the frozen ux induction equation by co-estimating a core magnetic eld model and a ow model at the top of the outer core. The ow model is required to have smooth spatial and temporal behavior. The implementation of such constraints and their effects on a magnetic eld model built from one year of CHAMP satellite and observatory data, are presented. In particular, it is shown that the chosen constraints are ef cient and can be used to build reliable core magnetic eld secular variation and acceleration model components.

[1] We present a new method for estimating core surface flows by relaxing the tangentially geostrophic (TG) constraint. Ageostrophic flows are allowed if they are consistent with the radial component of the vorticity equation under assumptions of the magnetostrophic force balance and an insulating mantle. We thus derive a tangentially magnetostrophic (TM) constraint for flows in the spherical harmonic domain and implement it in a least squares inversion of GRIMM-2, a recently proposed core field model, for temporally continuous core flow models (2000.0-2010.0). Comparing the flows calculated using the TG and TM constraints, we show that the number of degrees of freedom for the poloidal flows is notably increased by admitting ageostrophic flows compatible with the TM constraint. We find a significantly improved fit to the GRIMM-2 secular variation (SV) by including zonal poloidal flow in TM flow models. Correlations between the predicted and observed length-of-day variations are equally good under the TG and TM constraints. In addition, we estimate flow models by imposing the TM constraint together with other dynamical constraints: either purely toroidal (PT) flow or helical flow constraint. For the PT case we cannot find any flow which explains the observed SV, while for the helical case the SV can be fitted. The poor compatibility between the TM and PT constraints seems to arise from the absence of zonal poloidal flows. The PT flow assumption is likely to be negated when the radial magnetostrophic vorticity balance is taken into account, even if otherwise consistent with magnetic observations.

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