International Geomagnetic Reference Field - The Thirteenth Generation

Editorial Board (November 2022)
Editor-in-Chief
Takeshi Sagiya, Nagoya University, Japan

Vice Editors-in-Chief
Masahito Nosé, Nagoya University, Japan

Aitaro Kato, University of Tokyo, Japan

Editors
Koki Aizawa
Hideo Aochi
Pascal Audet
Kiyoshi Baba
Joseph B.H. Baker
Nanan Balan
Stephan Christoph Buchert
Sonia Calvari
Xiaowei ChenPeter Chi
Harold C. Connolly Jr
Phil Cummins
Hao Dong
Guangyu Fu
Hidenori Genda
Aditya Gusman
Tomasz Hadaś
Stuart Henrys
James Hickey
Hauke Hussmann

Mie Ichihara
Hidekatsu Jin
Art Jolly
Shunichi Kamata
Nobuki Kame
Katsuya Kaneko
Ikuo Katayama
Yoko Kebukawa
Kunihiro Keika
Kostas Konstantinou
Alexey Kuvshinov
Juanjo Ledo
Koji Matsuo
Yasunobu Miyoshi
Atsuko Namiki
Yasuhito Narita
Kazunari Nawa
Kiwamu Nishida
Hiroyo Ohya
Duggirala Pallamraju

Severine Rosat
Akinori Saito
Tatsuhiko Saito
David Shelly
Hisayoshi Shimizu
Wataru Suzuki
Youichiro Takada
Sunny Tam
Naoki Uchida
Yanbin Wang
Yih-Min Wu
Chuang Xuan
Takahiro Yamamoto
Yuhji Yamamoto
Tadashi Yamasaki
Yusuke Yokota
Yohei Yukutake
Seiji Zenitani

Hiroo Kanamori
Jun'ichiro Kawaguchi
Takafumi Matsui
Hitoshi Mizutani

Yasuo Ogawa
Toshitaka Tsuda
Zhongliang Wu
Kiyoshi Yomogida

Advisory Board
Benjamin Fong Chao
Bernard Chouet
Yoshimori Honkura
Toshihiko Iyemori

Journal Scope
Earth, Planets and Space (EPS) is the official journal of Society of Geomagnetism and Earth, Planetary
and Space Sciences, The Seismological Society of Japan, The Volcanological Society of Japan, The
Geodetic Society of Japan, and The Japanese Society for Planetary Sciences.
EPS is a peer-reviewed, open-access journal published under SpringerOpen. It is an international journal
covering scientific articles in the entire field of earth and planetary sciences, particularly geomagnetism,aeronomy, space science, seismology, volcanology, geodesy, and planetary science. EPS also welcomesarticles in new and interdisciplinary subjects, and technical reports on instrumentation and software.
The journal was launched in 1998 and has since published over 4000 articles. All of them are available forfree on SpringerLink:
https://link.springer.com/journal/40623/volumes-and-issues
More information about the journal, its article collections, and the submission process is available on thejournal homepage:https://earth-planets-space.springeropen.com
Submit your next research article to Earth, Planets and Space via:
https://www.editorialmanager.com/epsp
Yours sincerely,
Prof. Takeshi Sagiya
Editor-in-Chief, Earth, Planets and Space
eic@earth-planets-space.org

Earth, Planets and Space(2022) 74:11
Alken et al. Earth, Planets and Space
https://doi.org/10.1186/s40623-021-01569-z

Open Access

PREFACESpecial issue “International Geomagnetic
Reference Field: the thirteenth generation”
P. Alken1,2*, E. Thébault3, C. D. Beggan4 and M. Nosé5

2015.0. Twelve candidate models were received for theepoch 2020.0. And finally fourteen candidate models were received to forecast the field evolution overthe period 2020 to 2025. A task force was assembled toevaluate each candidate model and combine all candidates into a final set of model coefficients for IGRF-13.
The findings of this task force are documented in Alken
et al. (2021b). A summary of the final IGRF-13 model ispresented in Alken et al. (2021c). Each team who participated in IGRF-13 prepared manuscripts detailing theirwork, which are collected into this special issue. Below,
we provide a brief description of the methods used forbuilding their candidate models.
Brown et al. (2021) describes three candidate models
submitted by the British Geological Survey based on datafrom the European Swarm satellite mission and groundobservatories. They discuss their main field candidates
for 2015.0 and 2020.0 as well as a secular variation forecast (2020 to 2025) based on advection of the main fieldusing steady core surface flow modeling. They additionally provide a retrospective analysis of the IGRF-12 secular variation forecasts.
Yang et al. (2021) present the only IGRF-13 candidate
model which did not utilize data from the Swarm mission. Instead, they used measurements from the China
Seismo-Electromagnetic Satellite (CSES) to build a main
field candidate for epoch 2020.0 and performed a validation analysis comparing their model with the other candidate models for epoch 2020.0. The lead institute for thiscandidate is the China Earthquake Administration.
Pavón-Carrasco et al. (2020) present main field candidate models for epochs 2015.0 and 2020.0, as well
as a secular variation forecast for 2020 to 2025 submitted by the Universidad Complutense de Madrid. Theydeveloped a bootstrapping method to build models fromThe large-scale time-varying portion of Earth’s internal
magnetic field originates from a dynamo process inside
the outer core. This geodynamo drives changes in Earth’s
magnetic field on timescales ranging from less than 1
year to hundreds of millions of years. Monitoring thelarge-scale internal geomagnetic field and its temporalvariations is fundamental to improving our understanding of our planet’s interior dynamics, as well as maintaining and developing technology designed to utilize magnetic field observations for the benefit of society.
The International Geomagnetic Reference Field (IGRF)
is a mathematical representation of the large-scale, timevarying, internal part of Earth’s magnetic field. The IGRF
consists of a set of model coefficients which can be input
into a mathematical equation to produce the three vector components of the geomagnetic field from the surfaceof the core mantle boundary (about 2900 km below the
Earth’s surface), to low-Earth orbiting satellite altitudes.
The 13th generation IGRF (IGRF-13), which is the subject of this special issue, provides model coefficients from1900 to 2025, allowing a description of the geomagnetic
field over the past one and one quarter centuries. The
IGRF is a truly international collaboration, by which multiple teams of magnetic field experts submit candidate
model coefficients to improve past model predictions, aswell as make forecasts for the next 5 year period.
The 13th generation IGRF received a record number ofcandidate model submissions from a total of 15 international teams. Eleven candidate models were received to
update the geomagnetic field description at the epoch*Correspondence: alken@colorado.edu
1
Cooperative Institute for Research in Environmental Sciences, Universityof Colorado Boulder, 325 Broadway, E/NE42, Boulder, CO 80305, USA
Full list of author information is available at the end of the article© The Author(s) 2022. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which
permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to theoriginal author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images orother third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line
to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory
regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of thislicence, visit http://creativecommons.org/licenses/by/4.0/.

1

International Geomagnetic Reference Field - The Thirteenth Generation
Alken et al. Earth, Planets and Space(2022) 74:11

Page 2 of 4

Petrov and Bondar (2021) present the IGRF-13 candidates submitted by the Pushkov Institute of Terrestrial
Magnetism (IZMIRAN), which included main field candidates for epoch 2015.0 and 2020.0, as well as a secularvariation forecast for 2020 to 2025. Their approach was
to bin Swarm measurements into discrete cells covering
Earth’s surface and applying spherical harmonic analysis
to the resulting grid.
Minami et al. (2020) present an IGRF-13 candidate secular variation forecast for 2020 to 2025 developed by several research groups in Japan. Their methodology applieda data assimilation scheme to a magnetohydrodynamic(MHD) dynamo simulation code. Their data assimilation method incorporated measurements from CHAMP,
Swarm, and the ground observatory network.
Metman et al. (2020) detail a secular variation forecast candidate to IGRF-13 developed at the Universityof Leeds. They use secular variation estimates provided
by the CHAOS-6 model to fit a steady core flow model,
followed by fitting the residual to a magnetic diffusion
model in order to provide a forecast over the 2020 to2025 time period.
Sanchez et al. (2020) present the Max Planck Institutefor Solar System Research secular variation candidate for
IGRF-13. They use a sequential ensemble data assimilation method, with the ensembles consisting of parallel 3D
dynamo simulations. The input data to the assimilation
comes from the COV-OBS.x1 and Kalmag models.
The NASA candidates to IGRF-13 are detailed in two
publications in this special issue. Sabaka et al. (2020) present the latest development in the Comprehensive Model(CM) series, culminating in a model called CM6 which
includes Ørsted, SAC-C, CHAMP and Swarm satellites,
and ground observations. CM6 models not only the core
field, but also contributions from the lithosphere, ionosphere, magnetosphere, and oceanic tides. CM6 was used
to generate main field candidates for epochs 2015.0 and
2020.0. Tangborn et al. (2021) present a secular variation
forecast for 2020 to 2025 combining a geodynamo modelwith an ensemble Kalman filter. Various geomagnetic
field models are used as inputs to the data assimilation
scheme.
Baerenzung et al. (2020) detail the University of Potsdam candidate models for IGRF-13. They present amodel named Kalmag, which assimilates CHAMP and
Swarm data using a Kalman filter scheme, and has avalidity period spanning two decades. This team submitted main field candidates for epochs 2015.0 and 2020.0,
as well as a secular variation forecast for 2020 to 2025.
Wardinski et al. (2020) present the Université de Strasbourg’s candidate model submissions to IGRF-13. They
combine satellite and ground measurements to build
a continuous model of the main field and its secular

Swarm and ground observatory data which allowed
them to provide uncertainties on their candidate model
coefficients.
Alken et al. (2021a) detail the candidate models submitted by NOAA/NCEI and the University of Colorado.
They present main field candidates for epochs 2015.0 and
2020.0, as well as a secular variation forecast for 2020
to 2025. Swarm satellite measurements were their primary data source, supplemented by ground observatory
measurements for validation. They additionally provide a
retrospective assessment of their previous IGRF-12 candidate model.
Finlay et al. (2020) presents the CHAOS-7 geomagnetic
field model, which served as the parent model for theDanish Technical University candidates to IGRF-13. They
built a model spanning more than two decades using datafrom Ørsted, CHAMP, SAC-C, Cryosat-2, Swarm, andthe ground observatory network. In addition to discussing their IGRF-13 candidates, they analyze the recent
behavior of the South Atlantic Anomaly.
Rother et al. (2021) presents the Mag.num geomagnetic core field model developed at GeoForschungsZentrum (GFZ) Potsdam, which served as the parent modelfor that institute’s IGRF-13 candidates. This model used
Swarm and ground observatory data to construct candidates for the main field at 2015.0 and 2020.0 as well
as a secular variation forecast for 2020 to 2025. They
additionally analyze recent trends of the South Atlantic
Anomaly.
The Institut de Physique du Globe de Paris (IPGP)
provided three candidate models to IGRF-13 which aredetailed in three separate papers in this special issue.
Vigneron et al. (2021) presents a main field candidate
for epoch 2015.0 using the experimental vector mode on
Swarm’s absolute scalar magnetometer (ASM-V). Roppet al. (2020) presents a novel approach to core field estimation by combining a sequential modeling approach,a Kalman filter, and a correlation-based modeling step.
Their method was used for the IPGP main field candidate for epoch 2020.0. Fournier et al. (2021a) presents
the IPGP secular variation candidate model to IGRF-13
based on integrating an ensemble of 100 geodynamo
models between epochs 2019.0 and 2025.0, with eachensemble member differing only in initial conditions.
Huder et al. (2020) detail the candidate models to
IGRF-13 submitted by the Institut des Sciences de la
Terre (ISTerre). They construct a model named COVOBS.x2 covering the time period 1840 to 2020, integrating ground observatory data, satellite data, and older
surveys. This team submitted main field candidates forepochs 2015.0 and 2020.0, as well as a secular variation
forecast for 2020 to 2025.

2

Earth, Planets and Space
Alken et al. Earth, Planets and Space(2022) 74:11

Page 3 of 4variation from 1957 to 2020. This approach was used toderive main field candidates for 2015.0 and 2020.0, as
well as a secular variation forecast for 2020 to 2025 basedon a multi-variate singular spectrum analysis of the secular variation recorded over the past six decades.
Finally, Fournier et al. (2021b) contributed a Frontier letter to this special issue, on the topic of secularvariation forecasting. Recent satellite observations haverevealed significant short time-scale variations in thegeomagnetic field which are difficult to predict by routinely used methods to extrapolate current measurements several years into the future. These authors analyze
35 years of past IGRF secular variation forecasts and findthat the quality of 5-year forecasts deteriorates significantly during times of rapid geomagnetic field changes.
They review the current state-of-the-art methods inphysics-based forecasting of secular variation, discuss
lessons learned over the past several decades, and comment on possible future directions.
The task force thanks all the participants for providing their time, resources and expertise to create the main
field models and forecasts for this generation of the IGRF.
We also thank the many data providers for the freelyavailable scientific magnetic data, without which it would
not be possible to produce such high quality models.

for the 13th generation International Geomagnetic Reference Field. Earth
Planets Space 73(48):1–25. https://doi.org/10.1186/s40623-020-01281-4
Alken P, Thébault E, Beggan CD, Amit H, Aubert J, Baerenzung J, Bondar TN,
Brown W, Califf S, Chambodut A, Chulliat A, Cox G, Finlay CC, Fournier A,
Gillet N, Grayver A, Hammer MD, Holschneider M, Huder L, Hulot G, Jager
T, Kloss C, Korte M, Kuang W, Kuvshinov A, Langlais B, Léger JM, Lesur V,
Livermore PW, Lowes FJ, Macmillan S, Mound JE, Nair M, Nakano S, Olsen
N, Pavón-Carrasco FJ, Petrov VG, Ropp G, Rother M, Sabaka TJ, Sanchez S,
Saturnino D, Schnepf NR, Shen X, Stolle C, Tangborn A, Tøffner-Clausen
L, Toh H, Torta JM, Varner J, Vervelidou F, Vigneron P, Wardinski I, Wicht J,
Woods A, Yang Y, Zeren Z, Zhou B (2021c) International Geomagnetic Reference Field: the thirteenth generation. Earth Planets Space 73(49):1–25
Baerenzung J, Holschneider M, Wicht J, Lesur V, Sanchez S (2020) The Kalmag
model as a candidate for IGRF-13. Earth Planets Space 72(163):1–13.
https://doi.org/10.1186/s40623-020-01295-y
Brown W, Beggan CD, Cox G, Macmillan S (2021) The BGS candidate models
for IGRF-13 with a retrospective analysis of IGRF-12 secular variation
forecasts. Earth Planets Space 73(42):1–21. https://doi.org/10.1186/
s40623-020-01301-3
Finlay CC, Kloss C, Olsen N, Hammer MD, Tøffner-Clausen L, Grayver A, Kuvshinov A (2020) The CHAOS-7 geomagnetic field model and observedchanges in the South Atlantic Anomaly. Earth Planets Space 72(156):1–31.
https://doi.org/10.1186/s40623-020-01252-9
Fournier A, Aubert J, Lesur V, Ropp G (2021a) A secular variation candidate
model for IGRF-13 based on Swarm data and ensemble inverse geodynamo modelling. Earth Planets Space 73(43):1–16. https://doi.org/10.
1186/s40623-020-01309-9
Fournier A, Aubert J, Lesur V, Thébault E (2021b) Physics-based secular variation candidate models for the IGRF. Earth Planets Space 73(190):1–18.
https://doi.org/10.1186/s40623-021-01507-z
Huder L, Gillet N, Finlay CC, Hammer MD, Tchoungui H (2020) COV-OBS.
x2: 180 years of geomagnetic field evolution from ground-based andsatellite observations. Earth Planets Space. https://doi.org/10.1186/
s40623-020-01194-2
Metman MC, Beggan CD, Livermore PW, Mound JE (2020) Forecasting yearlygeomagnetic variation through sequential estimation of core flow andmagnetic diffusion. Earth Planets Space 72(149):1–16. https://doi.org/10.
1186/s40623-020-01193-3
Minami T, Nakano S, Lesur V, Takahashi F, Matsushima M, Shimizu H, Nakashima
R, Taniguchi H, Toh H (2020) A candidate secular variation modelfor IGRF-13 based on MHD dynamo simulation and 4DEnVar data
assimilation. Earth Planets Space 72(136):1–24. https://doi.org/10.1186/
s40623-020-01253-8
Pavón-Carrasco FJ, Marsal S, Torta JM, Catalán M, Martín-Hernández F, Tordesillas JM (2020) Bootstrapping Swarm and observatory data to generate
candidates for the DGRF and IGRF-13. Earth Planets Space 72(152):1–18
Petrov VG, Bondar TN (2021) IZMIRAN candidate field model for IGRF-13. Earth
Planets Space 73(46):1–4. https://doi.org/10.1186/s40623-020-01312-0
Ropp G, Lesur V, Baerenzung J, Holschneider M (2020) Sequential modellingof the Earth’s core magnetic field. Earth Planets Space. https://doi.org/10.
1186/s40623-020-01230-1
Rother M, Korte M, Morschhauser A, Vervelidou F, Matzka J, Stolle C (2021) The
Mag.num core field model as a parent for IGRF-13, and the recent evolution of the South Atlantic Anomaly. Earth Planets Space 73(50):1–17
Sabaka TJ, Tøffner-Clausen L, Olsen N, Finlay CC (2020) CM6: a comprehensive
geomagnetic field model derived from both CHAMP and swarm satellite
observations. Earth Planets Space 72(80):1–24. https://doi.org/10.1186/
s40623-020-01210-5
Sanchez S, Wicht J, Bärenzung J (2020) Predictions of the geomagnetic secularvariation based on the ensemble sequential assimilation of geomagnetic
field models by dynamo simulations. Earth Planets Space 72(157):1–20.
https://doi.org/10.1186/s40623-020-01279-y
Tangborn A, Kuang W, Sabaka TJ, Yi C (2021) Geomagnetic secular variation
forecast using the NASA GEMS ensemble Kalman filter: a candidate SVmodel for IGRF-13. Earth Planets Space 47:1–14. https://doi.org/10.1186/
s40623-020-01324-w
Vigneron P, Hulot G, Léger JM, Jager T (2021) Using improved Swarm’s experimental absolute vector mode data to produce a candidate Definitive
Geomagnetic Reference Field (DGRF) 2015.0 model. Earth Planets Space
73(197):1–10. https://doi.org/10.1186/s40623-021-01529-7

Authors’ contributions
PA is chair of the IAGA DIV V-MOD (2019–2023) and initiated, coordinated andorganised the call and delivery of the 13th generation of the IGRF. ET is former
chair (2015–2019). CB is present co-chair (2019–2023). All authors have readand approved the manuscript.
Availability of data and materials
Not applicable.

Declarations
Competing interests
The authors declare that they have no competing interests.
Author details
1
Cooperative Institute for Research in Environmental Sciences, Universityof Colorado Boulder, 325 Broadway, E/NE42, Boulder, CO 80305, USA. 2 NOAA
National Centers for Environmental Information, Boulder, CO, USA. 3 Laboratoire Magmas et Volcans, UCA, CNRS, Clermont-Ferrand, France. 4 British
Geological Survey, The Lyell Centre, Research Avenue South, Edinburgh EH14
4AP, UK. 5 Institute for Space-Earth Environmental Research (ISEE), Nagoya
University, Furo-cho, Chikusa-ku, Nagoya 464-8601, Japan.
Received: 24 December 2021 Accepted: 25 December 2021

References
Alken P, Chulliat A, Nair M (2021a) NOAA/NCEI and University of Colorado
candidate models for IGRF-13. Earth Planets Space 73(44):1–9. https://doi.
org/10.1186/s40623-020-01313-z
Alken P, Thébault E, Beggan C, Aubert J, Baerenzung J, Brown WJ, Califf S,
Chulliat A, Cox G, Finlay CC et al (2021b) Evaluation of candidate models

3International Geomagnetic Reference Field - The Thirteenth Generation
Alken et al. Earth, Planets and Space(2022) 74:11

Page 4 of 4

Wardinski I, Saturnino D, Amit H, Chambodut A, Langlais B, Mandea M,
Thébault E (2020) Geomagnetic core field models and secular variation forecasts for the 13th International Geomagnetic Reference Field(IGRF-13). Earth Planets Space 72(155):1–22. https://doi.org/10.1186/
s40623-020-01254-7
Yang Y, Hulot G, Vigneron P, Shen X, Zhima Z, Zhou B, Magnes W, Olsen N,
Tøffner-Clausen L, Huang J, Zhang X, Yuan S, Wang L, Cheng B, Pollinger
A, Lammegger R, Dai J, Lin J, Guo F, Yu J, Wang J, Wu Y, Zhao X, Zhu X(2021) The CSES Global Geomagnetic Field Model (CGGM): an IGRF typeglobal geomagnetic field model based on data from the China SeismoElectromagnetic Satellite. Earth Planets Space 73(45):1–21. https://doi.
org/10.1186/s40623-020-01316-w

Publisher’s NoteSpringer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

4Earth, Planets and SpaceFRONTIER LETTER

Open AccessPhysics-based secular variation candidate models for
the IGRF
Alexandre Fournier*, Julien Aubert, Vincent Lesur and Erwan Thébault
Earth, Planets and Space 2021, 73:190 DOI: 10.1186/s40623-021-01507-z
Received: 6 April 2021, Accepted: 25 August 2021, Published: 19 October 2021

Abstract
Each International Geomagnetic Reference Field (IGRF) model released under the auspices of the International Association of Geomagnetism andAeronomy 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 amathematical 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 thepredicted 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 inthe 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 toincorporate at least part of the processes responsible for short-term geomagnetic variations. In thisletter, 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 thatboth strategies resort to “input” models of the main field and its secular variation constructed fromobservations. 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 ofincorporating rapid physical processes into the analysis on the one hand, and the accuracy andquantification of the uncertainty impacting input models on the other hand.

Keywords: Earth’s magnetic field, Geomagnetic secular variation, Geomagnetic secular

acceleration, Dynamo: theory and simulation, Convection, Magnetohydrodynamic
waves, Inverse theory

Graphical abstract*Corresponding author: Alexandre Fournier, fournier@ipgp.fr

FULL PAPER

Open AccessCM6: a comprehensive geomagnetic field model derived
from both CHAMP and Swarm satellite observations
Terence J. Sabaka*, Lars Tøffner-Clausen, Nils Olsen and Christopher C. Finlay
Earth, Planets and Space 2020, 72:80 DOI: 10.1186/s40623-020-01210-5
Received: 25 February 2020, Accepted: 26 May 2020, Published: 5 June 2020

Abstract
From the launch of the Ørsted satellite in 1999, through the CHAMP mission from 2000 to 2010, and now with the Swarm
constellation mission starting in 2013, satellite magnetometry has provided excellent monitoring of the near-Earth magnetic
field regime. The advanced Comprehensive Inversion scheme has been applied to data before Swarm and to the Swarm data
itself, but now for the first time to all the satellite data in this new era, culminating in the CM6 model. The highlights of this model
include not only a continuous core magnetic field description over the entire time period 1999 to 2019.5 in good agreement with
the CHAOS model series, but the addition of
two new oceanic tidal magnetic sources: thelarger lunar elliptic semi-diurnal constituent N2
and the lunar diurnal constituent O1. CM6 isalso the parent model of the NASA/GSFC
candidates for the DGRF2015 and IGRF2020 in
response to the IGRF-13 call. This paper
provides a full report on the development of
CM6.

Keywords: Geomagnetism, Field modeling,
CHAMP and Swarm satellites,
Tides

Graphical abstract*Corresponding author: Terence J. Sabaka, terence.j.sabaka@nasa.gov
5International Geomagnetic Reference Field - The Thirteenth Generation

FULL PAPER

Open AccessA candidate secular variation model for IGRF-13 based on
MHD dynamo simulation and 4DEnVar data assimilation
Takuto Minami*, Shin’ya Nakano, Vincent Lesur, Futoshi Takahashi, Masaki Matsushima,
Hisayoshi Shimizu, Ryosuke Nakashima, Hinami Taniguchi and Hiroaki Toh
Earth, Planets and Space 2020, 72:136 DOI: 10.1186/s40623-020-01253-8
Received: 2 February 2020, Accepted: 19 August 2020, Published: 21 September 2020

Abstract
We have submitted a secular variation (SV) candidate model for the thirteenth generation of International Geomagnetic Reference Field
model (IGRF-13) using a data assimilation scheme and a magnetohydrodynamic (MHD) dynamo simulation code. This is the first contribution
to the IGRF community from research groups in Japan. A geomagnetic field model derived from magnetic observatory hourly means, andCHAMP and Swarm-A satellite data, has been used as input data to the assimilation scheme. We adopt an ensemble-based assimilation
scheme, called four-dimensional ensemble-based variational method (4DEnVar), which linearizes outputs of MHD dynamo simulation withrespect to the deviation from a dynamo state vector at an initial condition. The data vector for the assimilation consists of the poloidal scalarpotential of the geomagnetic field at the core surface and flow velocity field slightly below the core surface. Dimensionless time of numericalgeodynamo is adjusted to the actual time by comparison of secular variation time scales. For SV prediction, we first generate an ensemble ofdynamo simulation results from a free dynamo run. We then assimilate the ensemble to the data with a 10-year assimilation window throughiterations, and finally forecast future SV by the weighted sum of the future extension parts of the ensemble members. Hindcast of the method
for the assimilation window from 2004.50 to 2014.25 confirms that the linear
approximation holds for 10-year assimilation window with our iterative
ensemble renewal method. We demonstrate that the forecast performance ofour data assimilation and forecast scheme is comparable with that of IGRF-12
by comparing data misfits 4.5 years after the release epoch. For estimation of
our IGRF-13SV candidate model, we set assimilation window from 2009.50 to2019.50. We generate our final SV candidate model by linear fitting for theweighted sum of the ensemble MHD dynamo simulation members from2019.50 to 2025.00. We derive errors of our SV candidate model by one
standard deviation of SV histograms based on all the ensemble members.

Keywords: IGRF, Secular variation, Geodynamo, Data assimilation, Coresurface flow, 4DEnVar

Graphical abstract*Corresponding author: Takuto Minami, tminami@port.kobe-u.ac.jp

FULL PAPER

Open Access

Forecasting yearly geomagnetic variation throughsequential estimation of core flow and magnetic diffusion
Maurits C. Metman, Ciarán D. Beggan, Philip W. Livermore and Jonathan E. Mound*
Earth, Planets and Space 2020, 72:149 DOI: 10.1186/s40623-020-01193-3
Received: 31 January 2020, Accepted: 4 May 2020, Published: 16 October 2020

Abstract
Earth’s internal magnetic field is generated through motion of the electrically conductive iron-alloy fluid comprising its outer core. Temporalvariability of this magnetic field, termed secular variation (SV), results from two processes: one is the interaction between core fluid motion andthe magnetic field, the other is magnetic diffusion. As diffusion is widely thought to take place over relatively long, millennial time scales, it iscommon to disregard it when considering yearly to decadal field changes; in this frozen-flux approximation, core fluid motion may be inferred on
the core–mantle boundary (CMB) using observations of SV at Earth’s surface. Such flow models
have been used to forecast variation in the magnetic field. However, recent work suggests that
diffusion may also contribute significantly to SV on short time scales provided that the radial
length scale of the magnetic field structure within the core is sufficiently short. In this work, we
introduce a hybrid method to forecast field evolution that considers a model based on both asteady flow and diffusion, in which we adopt a two-step process: first fitting the SV to a steadyflow, and then fitting the residual by magnetic diffusion. We assess this approach by hindcasting
the evolution for 2010–2015, based on fitting the models to CHAOS-6 using time windows prior to2010. We find that including diffusion yields a reduction of up to 25% in the global hindcast error
at Earth’s surface; at the CMB this error reduction can be in excess of 77%. We show that fitting themodel over the shortest window that we consider, 2009–2010, yields the lowest hindcast error.
Based on our hindcast tests, we present a candidate model for the SV over 2020–2025 for IGRF-13,
fit over the time window 2018.3–2019.3. Our forecasts indicate that over the next decade the axial
dipole will continue to decay, reversed-flux patches will increase in both area and intensity, andthe north magnetic (dip) pole will continue to migrate towards Siberia.

Keywords: Geomagnetism, Secular variation, Frozen flux, diffusion

Graphical abstract*Corresponding author: Jonathan E. Mound, J.E.Mound@leeds.ac.uk
6

Earth, Planets and Space

FULL PAPER

Open Access

Bootstrapping Swarm and observatory data to generate
candidates for the DGRF and IGRF-13
F. Javier Pavón-Carrasco*, Santiago Marsal, J. Miquel Torta, Manuel Catalán,Fátima Martín-Hernández and J. Manuel Tordesillas
Earth, Planets and Space 2020, 72:152 DOI: 10.1186/s40623-020-01198-y
Received: 27 January 2020, Accepted: 18 May 2020, Published: 21 October 2020

Abstract

-1

0 1

2

3

4

5

6 7 8
SH order, m

9

10 11 12 13

0.3
0.2
0.1

0 1

3

2

5

4

6 7 8
SH order, m

9

0

10 11 12 13...g h g h2

1

SH degree, n

4
5
6
7
8
9
10
11
12
13

0

-1

1010

PS and difference at the
Earth’s surface (nT 2 )g g h g h ...

1

1010

108

108

106
10

4

106

102

104

Open Access

100

Sequential modelling of the Earth’s core magnetic field
0 1

2

3

4

5

6 7 8
SH order, m

9

10 11 12 13

-2

10-2

PS and difference at CMB (nT2 )Power Spectra of IGRF candidate vs IGRF-2020
c IGRF candidate vs. IGRF-2020 (di fference of Gauss coeff.)
Graphicald abstract*Corresponding author: F. Javier Pavón-Carrasco,32 fpavon@ucm.es

FULL PAPER

-2

6
7
8
9
10
11
12
13

Gauss coef. uncertainty (nT)0

SH degree, n1

Log10(Gauss coefficients, nT)

Geomagnetic fieldmodelling, Secular variation,
IGRF, Swarm, Geomagnetic
observatories

6
7
8
9
10
11
12
13

Gauss coeff. difference (nT)

Keywords: Geomagnetic field,

SH degree, nAs posted by the Working Group V of the International Association of Geomagnetism and Aeronomy (IAGA), the 13th
generation of the International Geomagnetic Reference Field (IGRF) has been released at the end of 2019. Following IAGA
recommendations, in this work we present a candidate model for the IGRF-13, for which we have used the available Swarmsatellite and geomagnetic observatory ground data for the last year. In order to provide the IGRF-13 candidate, we haveextrapolated the Gauss coefficients of the main field and its secular variation to January 1st, 2020. In addition, we havegenerated a Definitive Geomagnetic Reference Field model for 2015.0 using the same modelling approach, but focussed on a
1-year time window of data centred on 2015.0. To jointly model both satellite and ground data, we have followed the classicalprotocols and data filters applied in geomagnetic field modelling. Novelty arrives from the application of bootstrap analysis tosolve issues related to the inhomogeneityof the spatial and temporal data
Gauss
Gausscoefficientscoefficientsfor
forIGRFIGRFcandidate
candidate
Gauss
Gausscoefficient
coefficientuncertainty
uncertaintyofofIGRF
IGRFcandidate
candidate
distributions. This new approach allows
g g h g h ...
...g h g h
g g h g h ...
...g h g h
0.6
4
1
1
the estimation of not only the Gauss
2
2
0.5
3
3
3
4
4
coefficients, but also their uncertainties.
0.4
2
5
5

2

4

102

6

8

SH degree, n1012Guillaume Ropp*, Vincent Lesur, Julien Baerenzung and Matthias Holschneider
Earth, Planets and Space 2020, 72:153 DOI: 10.1186/s40623-020-01230-1
Received: 19 March 2020, Accepted: 8 July 2020, Published: 21 October 2020

Abstract
We describe a new, original approach to the modelling of the Earth’s magnetic field. The overall objective of this study is toreliably render fast variations of the core field and its secular variation. This method combines a sequential modelling approach, aKalman filter, and a correlation-based modelling step. Sources that most significantly contribute to the field measured at thesurface of the Earth are modelled. Their separation is based on strong prior information on their spatial and temporal behaviours.
We obtain a time series of model distributions which display behaviours similar to those of recent models based on more classic
approaches, particularly at large temporal and spatial scales. Interesting new features and periodicities are visible in our models
at smaller time and spatial scales. An important aspect of our method is to yield reliable error bars for all model parameters. Theseerrors, however, are only as reliable as the description of the different sources and the prior information used are realistic. Finally,
we used a slightly different version of our method to produce candidate models for the thirteenth edition of the International
Geomagnetic Reference Field.

Keywords: Geomagnetic field,
Secular variation,
Kalman filter, IGRF

Fig. 1*Corresponding author: Guillaume Ropp, ropp@ipgp.fr
7

60˚

60˚

60˚

60˚

30˚

30˚

30˚

30˚

0˚
International Geomagnetic Reference Field- 0˚The Thirteenth Generation

0˚

FULL PAPER−30˚

−30˚

0˚

Open Access
−30˚

−30˚

Geomagnetic core field models andsecular variation forecasts
1969
for the 13th International Geomagnetic Reference Field(IGRF-13)
−60˚

−60˚

−60˚

1969

−60˚

[x106 nT]

−1.0

−0.5

0.0

0.5

1.0

−3

−2

−1

0

1

2

60˚
60˚
I. Wardinski*, D. Saturnino,
H. Amit, A. Chambodut,60˚B. Langlais, M. Mandea andE. Thébault[x104nT/yr]
3

60˚

30˚
30˚
Earth, Planets and30˚Space 2020, 72:155 DOI: 10.1186/s40623-020-01254-7
Received: 30 April 2020, Accepted: 19 August 2020, Published: 22 October 2020

Abstract

0˚

0˚

30˚

0˚

0˚

−30˚ at satellite−30˚−30˚the geomagnetic field taken at Earth’s surface and−30˚
Observations ofaltitude are combined to construct continuous
models of the geomagnetic field and its secular variation from 1957 to 2020. From these parent models, we derive candidate
−60˚
−60˚
−60˚
−60˚
2010
main field models for the epochs 2015 and 2020 to the 13th generationof the International Geomagnetic Reference Field2010(IGRF). The secular variation candidate model for the period[x102020–2025
is derived from a forecast of the secular variationinnT][x10 nT/yr]
2022.5, which results froma multi-variate
analysis of the secularfrom 1957
to1 2020.
−1.0−0.5
0.0 singular
0.5 spectrum
1.0−3 variation
−2
−1
0
2
3
6

4

Keywords: The geomagnetic
field, Geomagnetic secularvariation,
60˚
60˚
Geomagnetic field models, Forecasts of the
30˚
geomagnetic
field

30˚

30˚

0˚

0˚

−30˚

−30˚

−60˚

−60˚

60˚

60˚

30˚

0˚

0˚

−30˚

−30˚

2020

−60˚

2020

−60˚

[x106 nT]
−1.0

−0.5

0.0

0.5

1.0

[x104nT/yr]
−3

−2

−1

0

1

2

3

Graphical abstract*Corresponding author: I. Wardinski, wardinski@unistra.fr

FULL PAPER

Open Access

The CHAOS-7 geomagnetic field model and observed changes
in the South Atlantic Anomaly
Christopher C. Finlay*, Clemens Kloss, Nils Olsen, Magnus D. Hammer, Lars Tøffner-Clausen,
Alexander Grayver and Alexey Kuvshinov
Earth, Planets and Space 2020, 72:156 DOI: 10.1186/s40623-020-01252-9
Received: 5 May 2020, Accepted: 17 August 2020, Published: 20 October 2020

Abstract
We present the CHAOS-7 model of the time-dependent near-Earth geomagnetic field between 1999 and 2020 based on magnetic field observations
collected by the low-Earth orbit satellites Swarm, CryoSat-2, CHAMP, SAC-C and Ørsted, and on annual differences of monthly means of groundobservatory measurements. The CHAOS-7 model consists of a time-dependent internal field up to spherical harmonic degree 20, a static internal field
which merges to the LCS-1 lithospheric field model above degree 25, a model of the magnetospheric field and its induced counterpart, estimates ofEuler angles describing the alignment of satellite vector magnetometers, and magnetometer calibration parameters for CryoSat-2. Only data from dark
regions satisfying strict geomagnetic quiet-time criteria (including conditions on IMF Bz and By at all latitudes) were used in the field estimation. Modelparameters were estimated using an iteratively reweighted regularized least-squares procedure; regularization of the time-dependent internal field
was relaxed at high spherical harmonic degree compared with previous versions of the CHAOS model. We use CHAOS-7 to investigate recent changes
in the geomagnetic field, studying the evolution of the South Atlantic weak field anomaly and rapid field changes in the Pacific region since 2014. At
Earth’s surface a secondary minimum of the South Atlantic Anomaly is now evident to the south
west of Africa. Green’s functions relating the core–mantle boundary radial field to the surface
intensity show this feature is connected with the movement and evolution of a reversed flux
feature under South Africa. The continuing growth in size and weakening of the main anomaly islinked to the westward motion and gathering of reversed flux under South America. In the Pacificregion at Earth’s surface between 2015 and 2018 a sign change has occurred in the second time
derivative (acceleration) of the radial component of the field. This acceleration change took theform of a localized, east–west oriented, dipole. It was clearly recorded on ground, for example atthe magnetic observatory at Honolulu, and was seen in Swarm observations over an extended
region in the central and western Pacific. Downward continuing to the core–mantle boundary, we
find this event originated in field acceleration changes at low latitudes beneath the central andwestern Pacific in 2017.

Keywords: Geomagnetism, Secular variation, Field modelling, South Atlantic Anomaly, Swarm*Corresponding author: Christopher C. Finlay, cfinlay@space.dtu.dk
8Graphical abstract

Earth, Planets and Space

FULL PAPER

Open AccessPredictions of the geomagnetic secular variation based on
the ensemble sequential assimilation of geomagnetic fieldmodels by dynamo simulations
Sabrina Sanchez*, Johannes Wicht and Julien Bärenzung
Earth, Planets and Space 2020, 72:157 DOI: 10.1186/s40623-020-01279-y
Received: 17 April 2020, Accepted: 23 September 2020, Published: 22 October 2020

Abstract
The IGRF offers an important incentive for testing algorithms predicting the Earth’s magnetic field changes, known as secular variation (SV), in
a 5-year range. Here, we present a SV candidate model for the 13th IGRF that stems from a sequential ensemble data assimilation approach(EnKF). The ensemble consists of a number of parallel-running 3D-dynamo simulations. The assimilated data are geomagnetic field snapshots
covering the years 1840 to 2000 from the COV-OBS.x1 model and for 2001 to 2020 from the Kalmag model. A spectral covariance localization
method, considering the couplings between spherical harmonics of the same equatorial symmetry and same azimuthal wave number, allows
decreasing the ensemble size to about a 100 while maintaining the stability of the assimilation. The quality of 5-year predictions is tested forthe past two decades. These tests show that the assimilation scheme is able to reconstruct the overall SV evolution. They also suggest that abetter 5-year forecast is obtained keeping the SV constant compared to the dynamically evolving SV. However, the quality of the dynamical
forecast steadily improves over the full assimilation window (180years). We therefore propose the instantaneous SV estimate for2020 from our assimilation as a candidate model for the
IGRF-13. The ensemble approach provides uncertainty
estimates, which closely match the residual differences withrespect to the IGRF-13. Longer term predictions for the evolutionof the main magnetic field features over a 50-year range are alsopresented. We observe the further decrease of the axial dipole ata mean rate of 8 nT/year as well as a deepening and broadeningof the South Atlantic Anomaly. The magnetic dip poles are seen
to approach an eccentric dipole configuration.

Keywords: Earth’s magnetic field, Geomagnetic secularvariation, Dynamo simulations, Data assimilation

Graphical abstract*Corresponding author: Sabrina Sanchez, sanchezs@mps.mpg.de

FULL PAPER

Open Access

COV-OBS.x2: 180 years of geomagnetic field evolution
from ground-based and satellite observationsLoïc Huder, Nicolas Gillet*, Christopher C. Finlay, Magnus D. Hammer and Hervé Tchoungui
Earth, Planets and Space 2020, 72:160 DOI: 10.1186/s40623-020-01194-2
Received: 4 February 2020, Accepted: 8 May 2020, Published: 23 October 2020

Abstract
We present the geomagnetic field model COV-OBS.x2 that covers the period 1840–2020. It is primarily constrained byobservatory series, satellite data, plus older surveys. Over the past two decades, we consider annual differences of 4-monthly
means at ground-based stations (since 1996), and virtual observatory series derived from magnetic data of the satellite missions
CHAMP (over 2001–2010) and Swarm (since 2013). A priori information is needed to complement the constraints carried bygeomagnetic records and solve the ill-posed geomagnetic inverse problem. We use for this purpose temporal cross-covariances
associated with auto-regressive stochastic processes of order 2, whose parameters are chosen so as to mimic the temporal power
spectral density observed in paleomagnetic and observatory series. We aim this way to obtain as far as possible realistic posterior
model uncertainties. These can be used to infer for instance the core dynamics through data assimilation algorithms, or anenvelope for short-term magnetic field forecasts. We showthat because of the projection onto splines, one needs toinflate the formal model error variances at the most recent
epochs, in order to account for unmodeled high frequency
core field changes. As a by-product of the core field model, we
co-estimate the external magnetospheric dipole evolution on
periods longer than 2 years. It is efficiently summarized as thesum of a damped oscillator (of period 10.5 years and decayrate 55 years), plus a short-memory (6 years) damped random
walk.

Keywords: Geomagnetic field, Secular variation, Stochastic
equations, Model uncertainties

Graphical abstract*Corresponding author: Nicolas Gillet, nicolas.gillet@univ-grenoble-alpes.fr
9International Geomagnetic Reference Field - The Thirteenth Generation

FULL PAPER

Open Access

The Kalmag model as a candidate for IGRF-13
Julien Baerenzung*, Matthias Holschneider, Johannes Wicht, Vincent Lesur and Sabrina Sanchez
Earth, Planets and Space 2020, 72:163 DOI: 10.1186/s40623-020-01295-y
Received: 24 June 2020, Accepted: 13 October 2020, Published: 29 October 2020

Abstract
We present a new model of the geomagnetic field spanning the last 20 years and called Kalmag. Deriving from theassimilation of CHAMP and Swarm vector field measurements, it separates the different contributions to the observable field
through parameterized prior covariance matrices. To make the inverse problem numerically feasible, it has beensequentialized in time through the combination of a Kalman filter and a smoothing algorithm. The model provides reliable
estimates of past, present and future mean fields and associated uncertainties. The version presented here is an update of our
IGRF candidates; the amount of assimilated data
has been doubled and the considered time
window has been extended from [2000.5,
2019.74] to [2000.5, 2020.33].

Keywords: Geomagnetic field, Secularvariation, Assimilation, Kalmanfilter, Machine learning

Graphical abstract*Corresponding author: Julien Baerenzung, baerenzung@gmx.de

FULL PAPER

Open Access

The BGS candidate models for IGRF-13 with a retrospective
analysis of IGRF-12 secular variation forecasts
William J. Brown*, Ciarán D. Beggan, Grace A. Cox and Susan Macmillan
Earth, Planets and Space 2021, 73:42 DOI: 10.1186/s40623-020-01301-3
Received: 19 May 2020, Accepted: 22 October 2020, Published: 11 February 2021

Abstract
The three candidate models submitted by the British Geological Survey for the 13th generation International Geomagnetic Reference
Field are described. These DGRF and IGRF models are derived from vector and scalar magnetic field data from the European Space
Agency Swarm satellites and ground observatories, covering the period 2013.9 to 2019.7. The internal field model has time dependence
for degrees 1 to 15, represented by order 6 B-splines with knots at six monthly intervals. We also solve for a degree 1 external field timedependence describing annual and semi-annual signals with additional dependence on a bespoke Vector Magnetic Disturbance index.
Satellite data are weighted by spatial density, along-track standard deviations, anda larger-scale noise estimator defined in terms of a measure of Local Area Vector
Activity at the geographically closest magnetic observatories to the sampled
datum. Forecasting of the magnetic field secular variation for 2020–2025 is byadvection of the main field using steady core surface flows with steadyacceleration applied. We also investigate the performance of the previous
generation of candidate secular variation models, for IGRF-12, analysing theagreement of the candidates between 2015 and 2020 with the retrospective
IGRF-13. We find that there is no clear distinction between the performance ofmathematically and physically extrapolated forecasts in the period 2015–2020. We
confirm that the methodology for the BGS IGRF-12 predictions performed well,
despite observed secular accelerations that are highlighted by our analysis, andthus justify the methodology used for our IGRF-13 SV candidate.

Keywords: International Geomagnetic Reference Field, Geomagnetism,
Secular variation

Graphical abstract*Corresponding author: William J. Brown, wb@bgs.ac.uk
10

Earth, Planets and Space

FULL PAPER

Open AccessA secular variation candidate model for IGRF-13 based on
Swarm data and ensemble inverse geodynamo modelling
Alexandre Fournier*, Julien Aubert, Vincent Lesur and Guillaume Ropp
Earth, Planets and Space 2021, 73:43 DOI: 10.1186/s40623-020-01309-9
Received: 31 January 2020, Accepted: 5 November 2020, Published: 11 February 2021

Abstract
This paper describes the design of a candidate secular variation model for the 13th generationof the International Geomagnetic Reference Field. This candidate is based upon the integrationof an ensemble of 100 numerical models of the geodynamo between epochs 2019.0 and
2025.0. The only difference between each ensemble member lies in the initial condition that isused for the numerical integration, all other control parameters being fixed. An initial condition
is defined as follows: an estimate of the magnetic field and its rate-of-change at the coresurface for 2019.0 is obtained from a year (2018.5–2019.5) of vector Swarm data. This estimate(common to all ensemble members) is subject to prior constraints: the statistical properties of
the numerical dynamo model for the main geomagnetic field and its secular variation, andprescribed covariances for the other sources. One next considers 100 three-dimensional corestates (in terms of flow, buoyancy and magnetic fields) extracted at different discrete times
from a dynamo simulation that is not constrained by observations, with the time distance
between each state exceeding the dynamo decorrelation time. Each state is adjusted (in three
dimensions) in order to take the estimate of the geomagnetic field and its rate-of-change for2019.0 into account. This methodology provides 100 different initial conditions for subsequent
numerical integration of the dynamo model up to epoch 2025.0. Focussing on the 2020.0–
2025.0 time window, we use the median average rate-of-change of each Gauss coefficient of
the ensemble and its statistics to define the geomagnetic secular variation over that timeframe and its uncertainties.

Keywords: Earth’s magnetic field, Geomagnetic secular variation, Satellite magnetics,
Dynamo: theory and simulation, Inverse theory

Graphical abstract*Corresponding author: Alexandre Fournier, fournier@ipgp.fr

FULL PAPER

Open Access

NOAA/NCEI and University of Colorado candidate models
for IGRF-13
P. Alken*, A. Chulliat and M. Nair
Earth, Planets and Space 2021, 73:44 DOI: 10.1186/s40623-020-01313-z
Received: 7 September 2020, Accepted: 10 November 2020, Published: 11 February 2021

Abstract
The International Geomagnetic Reference Field (IGRF) is a set of parameters representing the large-scale internal part of Earth’s
magnetic field. The 13th generation IGRF requested candidate models for adefinitive main field for 2015.0, a provisional main field for 2020.0, and a
predictive secular variation covering the period 2020.0–2025.0. The
University of Colorado (CU) and the National Centers for Environmental
Information (NCEI), part of the National Oceanic and Atmospheric
Administration (NOAA), have produced these three candidate models forconsideration in IGRF-13. In this paper, we present the methodology used toderive our candidate models. Our candidates were built primarily from
Swarm satellite data, and also relied on geomagnetic indices derived fromthe ground observatory network. The ground observatories played a crucialrole as independent data in validating our candidates. This paper also
provides a retrospective assessment of the CU/NCEI candidate model to theprevious IGRF (IGRF-12) and discusses the impact of differences between
candidate and final IGRF models on global model errors.

Keywords: IGRF, Magnetic field modeling, Geomagnetism
Graphical abstract*Corresponding author: P. Alken, alken@colorado.edu
11International Geomagnetic Reference Field - The Thirteenth Generation

FULL PAPER

Open Access

The CSES global geomagnetic field model (CGGM):
an IGRF-type global geomagnetic field model based on datafrom the China Seismo-Electromagnetic Satellite
Yanyan Yang, Gauthier Hulot*, Pierre Vigneron, Xuhui Shen*, Zeren Zhima, Bin Zhou, Werner Magnes,
Nils Olsen, Lars Tøffner-Clausen, Jianpin Huang, Xuemin Zhang, Shigeng Yuan, Lanwei Wang, Bingjun Cheng,
Andreas Pollinger, Roland Lammegger, Jianpin Dai, Jun Lin, Feng Guo, Jingbo Yu, Jie Wang, Yingyan Wu,
Xudong Zhao and Xinghong Zhu
Earth, Planets and Space 2021, 73:45 DOI: 10.1186/s40623-020-01316-w
Received: 12 March 2020, Accepted: 16 November 2020, Published: 11 February 2021

Abstract
Using magnetic field data from the China Seismo-Electromagnetic Satellite (CSES) mission, we derive a global geomagnetic field model, which
we call the CSES Global Geomagnetic Field Model (CGGM). This model describes the Earth’s magnetic main field and its linear temporal evolution
over the time period between March 2018 and September 2019. As the CSES mission was not originally designed for main field modelling, we
carefully assess the ability of the CSES orbits and data to provide relevant data for such a purpose. A number of issues are identified, and an
appropriate modelling approach is found to mitigate these. The resulting CGGM model appears to be of high enough quality, and it is next used
as a parent model to produce a main field model extrapolated to epoch 2020.0, which was eventually submitted on October 1, 2019 as one of the
IGRF-13 2020 candidate models. This CGGM candidate model, the first ever produced by a Chinese-led team, is also the only one relying on a data
set completely independent from that used by all other candidate models. A successful validation of this candidate model is performed bycomparison with the final (now published) IGRF-13 2020 model and all other candidate
models. Comparisons of the secular variation predicted by the CGGM parent model with thefinal IGRF-13 2020–2025 predictive secular variation also reveal a remarkable agreement.
This shows that, despite their current limitations, CSES magnetic data can already be used to
produce useful IGRF 2020 and 2020–2025 secular variation candidate models to contributeto the official IGRF-13 2020 and predictive secular variation models for the coming 2020–2025 time period. These very encouraging results show that additional efforts to improve the
CSES magnetic data quality could make these data very useful for long-term monitoring of
the main field and possibly other magnetic field sources, in complement to the data
provided by missions such as the ESA Swarm mission.

Keywords: CSES, CGGM, IGRF, Geomagnetism, Space magnetometry

Graphical abstract*Corresponding author: Gauthier Hulot, gh@ipgp.fr; Xuhui Shen, shenxh@seis.ac.cn

FULL PAPER

Open AccessGeomagnetic secular variation forecast using the NASA GEMS
ensemble Kalman filter: A candidate SV model for IGRF-13
Andrew Tangborn*, Weijia Kuang, Terence J. Sabaka and Ce Yi
Earth, Planets and Space 2021, 73:47 DOI: 10.1186/s40623-020-01324-w
Received: 22 July 2020, Accepted: 27 November 2020, Published: 11 February 2021

Abstract

Keywords: Geomagnetic Secular Variation, Data Assimilation,
Geodynamo Model

Mean Square Value

We have produced a 5-year mean secular variation (SV) of the geomagnetic field for the period 2020–2025. We use the NASA
Geomagnetic Ensemble Modeling System (GEMS), which consists of the NASA Goddard geodynamo model and ensemble
Kalman filter (EnKF) with 400 ensemble members. Geomagnetic field models are used as observations for the assimilation,
including gufm1 (1590–1960), CM4 (1961–2000) and CM6 (2001–2019).
Mean Square SV
The forecast involves a bias correction scheme that assumes that theCM6 SVmodel bias changes on timescales much longer than the forecast period,
Forecast SV
4
Extrapolation
10
so that they can be removed by successive forecast series. The algorithm
was validated on the time period 2010-2015 by comparing with CM6
before being applied to the 2020–2025 time period. This forecast has
been submitted as a candidate predictive model of IGRF-13 for the period
2020–2025.

10 3

2

3

4

5

L

Graphical abstract*Corresponding author: Andrew Tangborn, tangborn@umbc.edu
12

6

7

8

Earth, Planets and Space

FULL PAPER

Open AccessInternational Geomagnetic Reference Field: the thirteenth generation
P. Alken*, E. Thébault, C. D. Beggan, H. Amit, J. Aubert, J. Baerenzung, T. N. Bondar, W. J. Brown, S. Califf, A. Chambodut,
A. Chulliat, G. A. Cox, C. C. Finlay, A. Fournier, N. Gillet, A. Grayver, M. D. Hammer, M. Holschneider, L. Huder, G. Hulot,
T. Jager, C. Kloss, M. Korte, W. Kuang, A. Kuvshinov, B. Langlais, J.-M. Léger, V. Lesur, P. W. Livermore, F. J. Lowes,
S. Macmillan, W. Magnes, M. Mandea, S. Marsal, J. Matzka, M. C. Metman, T. Minami, A. Morschhauser,
J. E. Mound, M. Nair, S. Nakano, N. Olsen, F. J. Pavón-Carrasco, V. G. Petrov, G. Ropp, M. Rother, T. J. Sabaka,
S. Sanchez, D. Saturnino, N. R. Schnepf, X. Shen, C. Stolle, A. Tangborn, L. Tøffner-Clausen, H. Toh, J. M. Torta,
J. Varner, F. Vervelidou, P. Vigneron, I. Wardinski, J. Wicht, A. Woods, Y. Yang, Z. Zeren and B. Zhou
Earth, Planets and Space 2021, 73:49 DOI: 10.1186/s40623-020-01288-x
Received: 11 May 2020, Accepted: 3 October 2020, Published: 11 February 2021

Abstract
In December 2019, the International Association of
Geomagnetism and Aeronomy (IAGA) Division V Working Group(V-MOD) adopted the thirteenth generation of the International
Geomagnetic Reference Field (IGRF). This IGRF updates theprevious generation with a definitive main field model for epoch
2015.0, a main field model for epoch 2020.0, and a predictive
linear secular variation for 2020.0 to 2025.0. This letter provides
the equations defining the IGRF, the spherical harmoniccoefficients for this thirteenth generation model, maps ofmagnetic declination, inclination and total field intensity for theepoch 2020.0, and maps of their predicted rate of change for the2020.0 to 2025.0 time period.

Keywords: IGRF, Magnetic field modeling, Geomagnetism
Graphical abstract*Corresponding author: P. Alken, alken@colorado.edu

FULL PAPER

The Mag.num core field model as a parent for IGRF-13, andthe recent evolution of the South Atlantic Anomaly

Open AccessM. Rother*, M. Korte, A. Morschhauser, F. Vervelidou, J. Matzka and C. Stolle
Earth, Planets and Space 2021, 73:50 DOI: 10.1186/s40623-020-01277-0
Received: 30 April 2020, Accepted: 20 September 2020, Published: 11 February 2021

Abstract
We present the GFZ candidate field models for the 13th Generation International Geomagnetic Reference Field (IGRF-13). These candidates were
derived from the Mag.num.IGRF13 geomagnetic core field model, which is constrained by Swarm satellite and ground observatory data from
November 2013 to August 2019. Data were selected from magnetically quiet periods, and the model parameters have been obtained using an
iteratively reweighted inversion scheme approximating a robust modified Huber norm as a measure of misfit. The root mean square misfit of theMag.num.IGRF13 model to Swarm and observatory data is in the order of 3–5 nT for mid and low latitudes, with a maximum of 44 nT for thesatellite east component data at high latitudes. The time-varying core field is described by order 6 splines and spherical harmonic coefficients up
to degree and order 20. We note that the temporal variation of the core field component of the Mag.num.IGRF13 model is strongly damped
and shows a smooth secular variation that suits well for the IGRF, where secular variation is represented as constant over 5-year intervals. Further,
the external field is parameterised by a slowly varying part and a more rapidly varying part controlled by magnetic activity and interplanetary
magnetic field proxies. Additionally, the Euler angles of the magnetic field sensor orientation are co-estimated. A widely discussed feature of thegeomagnetic field is the South Atlantic Anomaly, a zone of weak and decreasing field strength stretching from southern Africa over to SouthAmerica. The IGRF and Mag.num.IGRF13 indicate that the anomaly has developed a second, less pronounced eastern minimum at Earth’s
surface since 2007. We observe that while the strong westernminimum continues to drift westwards, the less pronounced
eastern minimum currently drifts eastward at Earth’s surface. This
does not seem to be linked to any eastward motion at thecore–mantle boundary, but rather to intensity changes ofwestward drifting flux patches contributing to the observed
surface field. Also, we report a sudden change in the secularvariation measured at two South Atlantic observatories around2015.0, which occurred shortly after the well-known jerk of 2014.0.

Keywords: Geomagnetic field model, Main magnetic field,
South Atlantic Anomaly, Swarm, IGRF

Graphical abstract*Corresponding author: M. Rother, rother@gfz-potsdam.de13

International Geomagnetic Reference Field - The Thirteenth Generation

EXPRESS LETTER

Open Access

IZMIRAN candidate field model for IGRF-13
Valeriy G. Petrov* and Tatyana N. Bondar
Earth, Planets and Space 2021, 73:46 DOI: 10.1186/s40623-020-01312-0
Received: 14 August 2020, Accepted: 10 November 2020, Published: 11 February 2021

Abstract
The International Geomagnetic Reference Field (IGRF) model is a combination of the several models developed byindependent groups of scientists using different approaches for the selection of input data and methods for calculating
harmonic coefficients. This approach allows for mutual comparison of individual models and for their combination to obtainthe most reliable values of the harmonic coefficients. This letter provides a brief description of methods for building the
IZMIRAN Earth’s main magnetic field model, submitted to the IAGA Working Group V-MOD for creating IGRF-13. Special efforts
were made to obtain as uniform coverage of the entire Earth’s surface as possible with observations. The surface was divided
into a grid of approximately equal cells. Then the data for geomagnetically quiet intervals were placed in the corresponding
cells and a median filter was applied to select the data in each cell. Spherical harmonic coefficients up to degree 13 were
calculated for the interval 2014-Jan to2019-Aug with a time step of 10 days andextrapolated to 01.01.2010.

Keywords: IGRF, Magnetic fieldmodeling, Geomagnetism

Graphical abstract*Corresponding author: Valeriy G. Petrov, vpetrov@izmiran.ru

EXPRESS LETTER

Open AccessUsing improved Swarm’s experimental absolute vector mode
data to produce a candidate Definitive Geomagnetic
Reference Field (DGRF) 2015.0 model
Pierre Vigneron, Gauthier Hulot*, Jean-Michel Léger and Thomas Jager
Earth, Planets and Space 2021, 73:197 DOI: 10.1186/s40623-021-01529-7
Received: 8 July 2021, Accepted: 6 October 2021, Published: 25 October 2021

Abstract
We describe the way a global model of the geomagnetic field has been built using vector field data acquired by the absolute scalarmagnetometers (ASM) running in vector mode on board the Alpha and Bravo satellites of the European Space Agency (ESA) Swarm
mission. This model has been used as a parent model to build a candidate Definitive Geomagnetic Reference Field (DGRF) 2015.0
model to meet the call issued in the context of the recent update of the International Geomagnetic Reference Field (IGRF thirteenth
generation). Because small but systematic issues were identified in a previous candidate IGRF 2015.0 model built in the same spirit(also only relying on ASM vector field data) in the context of the previous IGRF update (IGRF twelfth generation), we now also use
improved ASM vector field (ASM-V) data. The issue originallyaffecting the ASM-V data is described, together with the way the
improved data are now being produced. The resulting candidate
DGRF 2015.0 model is shown to considerably improve on theprevious candidate IGRF 2015.0 model (being closer to the final
DGRF 2015.0 model by one order of magnitude in sphericalharmonic spectral terms). It is also shown to stand among thecandidate models closest to the final official DGRF 2015.0 model.
Being the only candidate DGRF 2015.0 model entirely and only
relying on such ASM-V data, it demonstrates the value of the new
ASM-V data for such global geomagnetic field modeling purposes.

Keywords: Geomagnetism, Magnetic field modeling, IGRF,

Swarm mission, Absolute vector magnetometers

Graphical abstract*Corresponding author: Gauthier Hulot, gh@ipgp.fr
14

Earth, Planets and SpaceTECHNICAL REPORT 

Open Access

Evaluation of candidate models for the 13th generation International
Geomagnetic Reference Field
P. Alken, E. Thébault*, C. D. Beggan, J. Aubert, J. Baerenzung, W. J. Brown, S. Califf, A. Chulliat, G. A. Cox,
C. C. Finlay, A. Fournier, N. Gillet, M. D. Hammer, M. Holschneider, G. Hulot, M. Korte, V. Lesur, P. W. Livermore,
F. J. Lowes, S. Macmillan, M. Nair, N. Olsen, G. Ropp, M. Rother, N. R. Schnepf, C. Stolle, H. Toh, F. Vervelidou,
P. Vigneron and I. Wardinski
Earth, Planets and Space 2021, 73:48 DOI: 10.1186/s40623-020-01281-4
Received: 8 July 2020, Accepted: 24 September 2020, Published: 11 February 2021

Abstract
In December 2019, the 13th revision of the International Geomagnetic Reference Field (IGRF) was released by the International Association of Geomagnetism
and Aeronomy (IAGA) Division V Working Group V-MOD. This revision comprises two new spherical harmonic main field models for epochs 2015.0 (DGRF2015) and 2020.0 (IGRF-2020) and a model of the predicted secular variation for the interval 2020.0 to 2025.0 (SV-2020-2025). The models were produced
from candidates submitted by fifteen international teams. These teams were led by the British Geological Survey (UK), China Earthquake Administration(China), Universidad Complutense de Madrid (Spain), University of Colorado Boulder (USA), Technical University of Denmark (Denmark), GFZ German
Research Centre for Geosciences (Germany), Institut de physique du globe de Paris (France), Institut des Sciences de la Terre (France), Pushkov Institute ofTerrestrial Magnetism, Ionosphere and Radio Wave Propagation (Russia), Kyoto University (Japan), University of Leeds (UK), Max Planck Institute for Solar
System Research (Germany), NASA Goddard Space Flight Center (USA), University of Potsdam(Germany), and Université de Strasbourg (France). The candidate models were evaluated individuallyand compared to all other candidates as well to the mean, median and a robust Huber-weighted
model of all candidates. These analyses were used to identify, for example, the variation between theGauss coefficients or the geographical regions where the candidate models strongly differed. The
majority of candidates were sufficiently close that the differences can be explained primarily by
individual modeling methodologies and data selection strategies. None of the candidates were so
different as to warrant their exclusion from the final IGRF-13. The IAGA V-MOD task force thus voted
for two approaches: the median of the Gauss coefficients of the candidates for the DGRF-2015 and
IGRF-2020 models and the robust Huber-weighted model for the predictive SV-2020-2025. In thispaper, we document the evaluation of the candidate models and provide details of the approach
used to derive the final IGRF-13 products. We also perform a retrospective analysis of the IGRF-12 SV
candidates over their performance period (2015–2020). Our findings suggest that forecasting secularvariation can benefit from combining physics-based core modeling with satellite observations.

Keywords: IGRF, Magnetic field modeling, Geomagnetism

Graphical abstract*Corresponding author: E. Thébault, erwan.thebault@univ-nantes.fr

15

Information for Contributors
General1.

Manuscripts should be submitted through the journal’s Editorial Manager system(https://www.editorialmanager.com/epsp/default.aspx).

2.

Only papers not previously published will be accepted, and the emphasis is on theoriginality of concept or observation.

3.

Five varieties of article types are available.
3.1“Full Paper” without word limit.

3.2“Express Letter” has a limit of 5000 words including the main text, figure legends
and table legends. The sum of the number of figures and tables should be lessthan or equal to 5.

3.3“Frontier Letter” can be submitted upon invitation by the Editor-in-Chief.

3.4“Technical Report” describes the technical development of instrument or software.

3.5“Comment” is a substantial re-analysis of a previously published article in thejournal. ”Comment” should not exceed 1000 words.

4.

Authors retain the copyright, and distribution of articles is free under the CC BY license.

Technical
1.

Manuscripts should be written in English with double spacing.

2.

Each manuscript should be organized in the following order: title, authors’ names,
affiliations, abstract, key words, main text, acknowledgement, appendix, references, andsupplementary materials. A graphical abstract image must be uploaded duringsubmission which should provide the reader with a visual description of the topic
covered in the article.

3.

The corresponding author should be clearly indicated.

4.

The abstract is limited to 350 words and should be informative and include principal
findings and conclusions. Please avoid abbreviations.

5.

The main text can have multiple free headings.

6.

High-resolution figures should be provided in the following format; PDF (preferred
format for diagrams), PNG (preferred format for photos or images), EPS ,TIFF, JPEG, BMP.
The graphical abstract should be approximately 920 × 300 pixels and should be
uploaded as a JPEG, PNG or SVG file.

7.

References must follow the Springer Basic style.

Correspondence
If you have any questions, please contact info@springeropen.com.

© EPS Steering Committee 2022 All rights reserved.
A Grant-in-Aid for Publication of Scientific Research Results (19HP1001) fromJapan Society for the Promotion of Science is used for printing.

Contents
Special issue “International Geomagnetic Reference Field: the thirteenth generation”.....................................................................................................................................................P. Alken, E. Thébault, C. D. Beggan and M. Nosé
Physics-based secular variation candidate models for the IGRF............................................................................................................ Alexandre Fournier, Julien Aubert, Vincent Lesur and Erwan Thébault
CM6: a comprehensive geomagnetic field model derived from both CHAMP and Swarm satellite observations................................................................................................ Terence J. Sabaka, Lars Tøffner-Clausen, Nils Olsen and Christopher C. Finlay
A candidate secular variation model for IGRF-13 based on MHD dynamo simulation and 4DEnVar data assimilation.............................................................................. Takuto Minami, Shin’ya Nakano, Vincent Lesur, Futoshi Takahashi, Masaki Matsushima,
Hisayoshi Shimizu, Ryosuke Nakashima, Hinami Taniguchi and Hiroaki Toh

Forecasting yearly geomagnetic variation through sequential estimation of core flow and magnetic diffusion..................................................................................... Maurits C. Metman, Ciarán D. Beggan, Philip W. Livermore and Jonathan E. Mound
Bootstrapping Swarm and observatory data to generate candidates for the DGRF and IGRF-13.................................................................................................... F. Javier Pavón-Carrasco, Santiago Marsal, J. Miquel Torta, Manuel Catalán,Fátima Martín-Hernández and J. Manuel Tordesillas

Sequential modelling of the Earth’s core magnetic field.............................................................................................Guillaume Ropp, Vincent Lesur, Julien Baerenzung and Matthias Holschneider
Geomagnetic core field models and secular variation forecasts for the 13th International Geomagnetic Reference Field(IGRF-13)......................................................I. Wardinski, D. Saturnino, H. Amit, A. Chambodut, B. Langlais, M. Mandea and E. Thébault
The CHAOS-7 geomagnetic field model and observed changes in the South Atlantic Anomaly............................................................................................................. Christopher C. Finlay, Clemens Kloss, Nils Olsen, Magnus D. Hammer,
Lars Tøffner-Clausen, Alexander Grayver and Alexey Kuvshinov

Predictions of the geomagnetic secular variation based on the ensemble sequential assimilation of geomagnetic fieldmodels by dynamo simulations.....................................................................Sabrina Sanchez, Johannes Wicht and Julien Bärenzung
COV-OBS.x2: 180 years of geomagnetic field evolution from ground-based and satellite observations....................................................................... Loïc Huder, Nicolas Gillet, Christopher C. Finlay, Magnus D. Hammer and Hervé Tchoungui
The Kalmag model as a candidate for IGRF-13.............................................................. Julien Baerenzung, Matthias Holschneider, Johannes Wicht, Vincent Lesur and Sabrina Sanchez
The BGS candidate models for IGRF-13 with a retrospective analysis of IGRF-12 secular variation forecasts.......................................................................................................... William J. Brown, Ciarán D. Beggan, Grace A. Cox and Susan Macmillan
A secular variation candidate model for IGRF-13 based on Swarm data and ensemble inverse geodynamo modelling............................................................................................................ Alexandre Fournier, Julien Aubert, Vincent Lesur and Guillaume Ropp
NOAA/NCEI and University of Colorado candidate models for IGRF-13 ...........................................P. Alken, A. Chulliat and M. Nair
The CSES global geomagnetic field model (CGGM): an IGRF-type global geomagnetic field model based on datafrom the China Seismo-Electromagnetic Satellite....................................... Yanyan Yang, Gauthier Hulot, Pierre Vigneron, Xuhui Shen, Zeren Zhima, Bin Zhou, Werner Magnes, Nils Olsen,
Lars Tøffner-Clausen, Jianpin Huang, Xuemin Zhang, Shigeng Yuan, Lanwei Wang, Bingjun Cheng,
Andreas Pollinger, Roland Lammegger, Jianpin Dai, Jun Lin, Feng Guo, Jingbo Yu, Jie Wang,
Yingyan Wu, Xudong Zhao and Xinghong Zhu

1
5
5

6
6

7
7
8

8
9
9
10
10
11
11

12

Geomagnetic secular variation forecast using the NASA GEMS ensemble Kalman filter: A candidate SV model for IGRF-13........................................................................................................................... Andrew Tangborn, Weijia Kuang, Terence J. Sabaka and Ce Yi 12International Geomagnetic Reference Field: the thirteenth generation........................... P. Alken, E. Thébault, C. D. Beggan, H. Amit, J. Aubert, J. Baerenzung, T. N. Bondar, W. J. Brown, S. Califf, A. Chambodut,
A. Chulliat, G. A. Cox, C. C. Finlay, A. Fournier, N. Gillet, A. Grayver, M. D. Hammer, M. Holschneider, L. Huder, G. Hulot,
T. Jager, C. Kloss, M. Korte, W. Kuang, A. Kuvshinov, B. Langlais, J.-M. Léger, V. Lesur, P. W. Livermore, F. J. Lowes,
S. Macmillan, W. Magnes, M. Mandea, S. Marsal, J. Matzka, M. C. Metman, T. Minami, A. Morschhauser,
J. E. Mound, M. Nair, S. Nakano, N. Olsen, F. J. Pavón-Carrasco, V. G. Petrov, G. Ropp, M. Rother, T. J. Sabaka,
S. Sanchez, D. Saturnino, N. R. Schnepf, X. Shen, C. Stolle, A. Tangborn, L. Tøffner-Clausen, H. Toh, J. M. Torta,
J. Varner, F. Vervelidou, P. Vigneron, I. Wardinski, J. Wicht, A. Woods, Y. Yang, Z. Zeren and B. Zhou

13

The Mag.num core field model as a parent for IGRF-13, and the recent evolution of the South Atlantic Anomaly.................................................................................................... M. Rother, M. Korte, A. Morschhauser, F. Vervelidou, J. Matzka and C. Stolle 13
IZMIRAN candidate field model for IGRF-13................................................................................Valeriy G. Petrov and Tatyana N. Bondar 14
Using improved Swarm’s experimental absolute vector mode data to produce a candidate Definitive Geomagnetic
Reference Field (DGRF) 2015.0 model ..............................Pierre Vigneron, Gauthier Hulot, Jean-Michel Léger and Thomas Jager 14
Evaluation of candidate models for the 13th generation International Geomagnetic Reference Field..................................................... P. Alken, E. Thébault, C. D. Beggan, J. Aubert, J. Baerenzung, W. J. Brown, S. Califf, A. Chulliat, G. A. Cox,
C. C. Finlay, A. Fournier, N. Gillet, M. D. Hammer, M. Holschneider, G. Hulot, M. Korte, V. Lesur, P. W. Livermore,
F. J. Lowes, S. Macmillan, M. Nair, N. Olsen, G. Ropp, M. Rother, N. R. Schnepf, C. Stolle, H. Toh, F. Vervelidou,
P. Vigneron and I. Wardinski

15

Cover image: Alken, P. et al., Earth, Planets and Space 2021, 73:49 DOI: 10.1186/s40623-020-01288-x