Modelling the Earth’s core magnetic field under flow constraints

Abstract

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.

Decadal variability in core surface flows deduced from geomagnetic observatory monthly means

“…Similarly, the small clockwise eddy beneath the south-western Pacific Ocean is not generally a feature of models derived from satellite data -in fact, the tangentially geostrophic flow of Holme and Olsen (2006) has a weak clockwise eddy, but their toroidal flow has an anti-clockwise eddy in the same location (and, as noted above, features of this size are not well resolved by observatory data). Besides generally decreasing power spectra for both toroidal and poloidal flow components, and an approximately order-of-magnitude difference between the toroidal and poloidal power, the dominant feature of the spectra is the loss of power at toroidal degree 3 (e.g Holme and Olsen 2006;Lesur et al 2010;Lesur et al 2015;Baerenzung et al 2014Baerenzung et al , 2016, regardless of whether or not the flow is assumed tangentially geostrophic. All these features are present in our spectra, for both snapshot and moderately TO-like flows (Fig.…”

“…Rygaard-Hjalsted et al (2000) were the first to use a Monte Carlo Markov Chain approach, but computational resources at that time limited the applicability of the method; more recently, Baerenzung et al (2014) and Baerenzung et al (2016) used it to obtain a more reliable estimate of the posterior probability distribution. Lesur et al (2010) adopted an iterative approach, first estimating a field model from the data, then using it to determine a starting model for the flow in the traditional fashion, and finally co-estimating the field and flow iteratively from the starting field and flow models. These studies suggest that the effect of assumptions as to the nature of the flow have at least as large an effect on the resulting flow model as any uncertainty in the main field.…”

Geomagnetic secular variation violating the frozen-flux condition at the core surface

“…The method would then require a huge computation, while it is theoretically feasible if the scalar product we have defined for a certain epoch is somehow extended to involve the total time span. A practical and more comprehensive test of the observed field against the conditions would be to assess simultaneously the existence of reasonable MF, SV and flow models that are temporally continuous and compatible with the FF or FF+TG condition (Lesur et al, 2010). In constructing such a comprehensive field model, the SH domain approach would be an effective alternative to the modelling approaches directly allowing for the surface integral conditions in the spatial domain (Gubbins, 1984;Bloxham and Gubbins, 1986;Constable et al, 1993;O'Brien et al, 1997;Jackson et al, 2007).…”

Radial vorticity constraint in core flow modeling

“…It is of particular interest, from the point of view of core dynamics as well, whether there can be a core field model compatible with the TM constraint and the PT assumption while retaining a decent fit to observations. Then, one would have to perform a simultaneous modeling of the field, flow and poloidal current under the TM constraint, i.e., an extension of our recent field-flow coestimation under the frozen-flux assumption [Lesur et al, 2010a]. It should bring a firmer answer to the issue of the PT flow assumption, and in addition, a field model allowing for the dynamics near the core surface.…”

“…The first term denotes the norm for the spatial smoothness, for which we adapt the norm et al, 2009;Lesur et al, 2010a]. We do not choose the "strong norm" [Bloxham, 1988] which has been most commonly used [Holme and Olsen, 2006;Wardinski et al, 2008], because it may overdamp the small-scale flows.…”