Comment on “Can core‐surface flow models be used to improve the forecast of the Earth's main magnetic field?” by Stefan Maus, Luis Silva, and Gauthier Hulot

Spherical Slepian functions (or &#8216;Slepian functions&#8217;) are mathematical functions which can be used to decompose potential fields, as represented by spherical harmonics, into smaller regions covering part of a spherical surface. This allows a spatio-spectral trade-off between aliasing of the signal at the boundary edges while constraining it within a region of interest. While Slepian functions have previously been applied to geodetic and crustal magnetic data, this work further applies Slepian functions to flows on the core-mantle boundary. There are two main reasons for restricting flow models to certain parts of the core surface. Firstly, we have reason to believe that different dynamics operate in different parts of the core (such as under LLSVPs) while, secondly, the modelled flow is ambiguous over certain parts of the surface (when applying flow assumptions). Spherical Slepian functions retain many of the advantages of our usual flow description, concerning for example the boundary conditions it must satisfy, and allowing easy calculation of the power spectrum, although greater initial computational effort is required. In this work, we apply Slepian functions to core flow models by directly inverting from satellite virtual observatory magnetic data into regions of interest. We successfully demonstrate the technique and current short comings by showing whole core surface flow models, flow within a chosen region, and its corresponding complement. Unwanted spatial leakage is generated at the region edges in the separated flows but to less of an extent than when using spherical Slepian functions on existing flow models. The limited spectral content we can infer for core flows is responsible for most, if not all, of this leakage. Therefore, we present ongoing investigations into the cause of this leakage, and to highlight considerations when applying Slepian functions to core surface flow modelling.

Download Full-text

Variability of the topographic core-mantle torque calculated from core surface flow models

Physics of The Earth and Planetary Interiors ◽

10.1016/j.pepi.2005.09.002 ◽

2006 ◽

Vol 154 (1) ◽

pp. 85-111 ◽

Cited By ~ 5

Author(s):

S. Asari ◽

H. Shimizu ◽

H. Utada

Keyword(s):

Surface Flow ◽

Core Surface ◽

Flow Models

Download Full-text

Effect of core electrical conductivity on core surface flow models

Earth Planets and Space ◽

10.1186/s40623-020-01269-0 ◽

2020 ◽

Vol 72 (1) ◽

Author(s):

Masaki Matsushima

Keyword(s):

Boundary Layer ◽

Electrical Conductivity ◽

Lorentz Force ◽

Thermal Evolution ◽

Surface Flow ◽

Core Flow ◽

Core Surface ◽

Flow Models ◽

The Core ◽

The Earth

AbstractThe electrical conductivity of the Earth’s core is an important physical parameter that controls the core dynamics and the thermal evolution of the Earth. In this study, the effect of core electrical conductivity on core surface flow models is investigated. Core surface flow is derived from a geomagnetic field model on the presumption that a viscous boundary layer forms at the core–mantle boundary. Inside the boundary layer, where the viscous force plays an important role in force balance, temporal variations of the magnetic field are caused by magnetic diffusion as well as motional induction. Below the boundary layer, where core flow is assumed to be in tangentially geostrophic balance or tangentially magnetostrophic balance, contributions of magnetic diffusion to temporal variation of the magnetic field are neglected. Under the constraint that the core flow is tangentially geostrophic beneath the boundary layer, the core electrical conductivity in the range from $${10}^{5} ~\mathrm{S}~{\mathrm{m}}^{-1}$$ 10 5 S m - 1 to $${10}^{7}~ \mathrm{S}~{\mathrm{m}}^{-1}$$ 10 7 S m - 1 has less significant effect on the core flow. Under the constraint that the core flow is tangentially magnetostrophic beneath the boundary layer, the influence of electrical conductivity on the core flow models can be clearly recognized; the magnitude of the mean toroidal flow does not increase or decrease, but that of the mean poloidal flow increases with an increase in core electrical conductivity. This difference arises from the Lorentz force, which can be stronger than the Coriolis force, for higher electrical conductivity, since the Lorentz force is proportional to the electrical conductivity. In other words, the Elsasser number, which represents the ratio of the Lorentz force to the Coriolis force, has an influence on the difference. The result implies that the ratio of toroidal to poloidal flow magnitudes has been changing in accordance with secular changes of rotation rate of the Earth and of core electrical conductivity due to a decrease in core temperature throughout the thermal evolution of the Earth.

Download Full-text

A reduced stochastic model of core surface dynamics based on geodynamo simulations

Geophysical Journal International ◽

10.1093/gji/ggz313 ◽

2019 ◽

Vol 219 (1) ◽

pp. 522-539 ◽

Cited By ~ 9

Author(s):

N Gillet ◽

L Huder ◽

J Aubert

Keyword(s):

Magnetic Field ◽

Stochastic Model ◽

Secular Variation ◽

Radial Magnetic Field ◽

Core Flow ◽

Core Surface ◽

Flow Models ◽

Flow Acceleration ◽

Equatorial Belt ◽

Augmented State

SUMMARYWe make use of recent geodynamo simulations to propose a reduced stochastic model of the dynamics at the surface of Earth’s core. On decadal and longer periods, this model replicates the most energetic eigen directions of the geodynamo computation. Towards shorter timescales, it proposes a compensation for weaknesses of these simulations. This model furthermore accounts for the signature, in the geomagnetic secular variation, of errors of representativeness associated with unresolved processes. We incorporate the reduced stochastic model into a geomagnetic data assimilation algorithm—an augmented state ensemble Kalman filter—and apply it to re-analyse magnetic field changes over the period 1880–2015. Errors of representativeness appear to be responsible for an important fraction of the observed changes in the secular variation, as it is the case in the dynamo simulation.Recovered core surface motions are primarily symmetric with respect to the equator. We observe the persistence of the eccentric westward gyre over the whole studied era and vortices that partly follow isocontours of the radial magnetic field at the core surface. Our flow models provide a good fit to decadal changes in the length-of-day and predict its interannual variations over the period 1940–2005. The largest core flow acceleration patterns are found in an equatorial belt below 10° in latitude and are associated with non-axisymmetric features. No systematic longitudinal drift of acceleration patterns is found, even over the past decades where satellite data are available. The acceleration of the high-latitude westward jet in the Pacific hemisphere is, during the satellite era, a factor 5 smaller than previously reported and its structure shows some evidence for equatorial asymmetry. The era of continuous satellite records provides enhanced contrast on the rapid core flow variations. The proposed assimilation algorithm offers the prospect of evaluating Earth-likeness of geodynamo simulations.

Download Full-text

Physics-based secular variation candidate models for the IGRF

Earth Planets and Space ◽

10.1186/s40623-021-01507-z ◽

2021 ◽

Vol 73 (1) ◽

Author(s):

Alexandre Fournier ◽

Julien Aubert ◽

Vincent Lesur ◽

Erwan Thébault

Keyword(s):

Magnetic Field ◽

Satellite Data ◽

Secular Variation ◽

Surface Flow ◽

Lessons Learned ◽

Rate Of Change ◽

Main Magnetic Field ◽

Time Rate ◽

Gauss Coefficient

AbstractEach International Geomagnetic Reference Field (IGRF) model released under the auspices of the International Association of Geomagnetism and Aeronomy comprises a secular variation component that describes the evolution of the main magnetic field anticipated for the 5 years to come. Every Gauss coefficient, up to spherical harmonic degree and order 8, is assumed to undergo its own independent linear evolution. With a mathematical model of the core magnetic field and its time rate of change constructed from geomagnetic observations at hand, a standard prediction of the secular variation (SV) consists of taking the time rate of change of each Gauss coefficient at the final time of analysis as the predicted rate of change. The last three generations of the IGRF have additionally witnessed a growing number of candidate SV models relying upon physics-based forecasts. This surge is motivated by satellite data that now span more than two decades and by the concurrent progress in the numerical modelling of Earth’s core dynamics. Satellite data reveal rapid (interannual) geomagnetic features whose imprint can be detrimental to the quality of the IGRF prediction. This calls for forecasting frameworks able to incorporate at least part of the processes responsible for short-term geomagnetic variations. In this letter, we perform a retrospective analysis of the performance of past IGRF SV models and candidates over the past 35 years; we emphasize that over the satellite era, the quality of the 5-year forecasts worsens at times of rapid geomagnetic changes. After the definition of the time scales that are relevant for the IGRF prediction exercise, we cover the strategies followed by past physics-based candidates, which we categorize into a “‘core–surface flow” family and a “dynamo” family, noting that both strategies resort to “input” models of the main field and its secular variation constructed from observations. We next review practical lessons learned from our previous attempts. Finally, we discuss possible improvements on the current state of affairs in two directions: the feasibility of incorporating rapid physical processes into the analysis on the one hand, and the accuracy and quantification of the uncertainty impacting input models on the other hand.

Download Full-text