Physics-based secular variation candidate models for the IGRF

Alexandre Fournier,Erwan Thébault,Vincent Lesur,Julien Aubert

doi:10.1186/s40623-021-01507-z

Abstract

Each 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.

Highlights

Introduction and backgroundThis solicited letter deals with the secular variation component of the International Geomagnetic Reference Field (IGRF), which is used to predict the evolution of the main geomagnetic field during the 5 years that follow each quinquennial release of a new generation of the IGRF.The magnetic field at location r and epoch t1, B(r, t1), is related to its state at the same location and at an anchor epoch t0 by t1B(r, t1) = B(r, t0) + ∂t B(r, t) dt, (1)t0 where the time rate of change ∂t B is traditionally referred to as the secular variation (SV)
Satellite-based observation of the field since 1999 has allowed the largest scales ( l 8 ) of the secular acceleration to be estimated; the associated time scales are compatible with a constant value, τ sa ∼ 10 years (Lesur et al 2010; Christensen et al 2012), slightly smaller values are obtained for the most recent magnetic field models: we find for instance that τ sa = [11.1, 14.7, 7.2, 10.2, 6.1, 8.0, 7.5, 10.1] years for the first 8 spherical harmonic degrees according to the CHAOS-7.5 model (Finlay et al 2020), considering the average of Wl and Wl over the 1998.0–2020.0 time window
Before congratulating ourselves further, let us first recall the mixed conclusions drawn from the hindcasting experiments described above, and second note that the global analysis reveals that all forecasts missed the geomagnetic jerk that started early in 2014, following a pulse of secular acceleration that had peaked at the core surface in 2012–2013 (Torta et al 2015; Finlay et al 2016; Kotzé 2017; Soloviev et al 2017)

Summary

Introduction

T0 where the time rate of change ∂t B is traditionally referred to as the secular variation (SV). If this field is due to dynamo action alone, the SV in the dynamo region. For practical purposes connected with utilizing the Earth’s magnetic field, we place ourselves outside the Earth’s core, in a source-free region. Under the assumption that the mantle is an electrical insulator, changes of any of the three components of the magnetic field at a location r are linearly related to changes in the radial component of the field at the top of the core, that is the sphere of radius c = 3485 km.

Discussion

Conclusion