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Abstract The International Geomagnetic Reference Field (IGRF) is a multi-institute model of the Earth’s magnetic field, compactly described by sets of up to 195 spherical harmonic (Gauss) coefficients to degree and order 13, which allows the continuous evaluation of the field at any location and time on or above the surface. It is developed from satellite and ground-based magnetometer data and describes the large-scale variation of the magnetic field in space and time under quiet conditions. While much effort has been made on improving the forecast of the secular variation of the field over the 5-year intervals between release and renewal, less emphasis has been placed on understanding the spatial errors from a user point of view. In this study, we estimate the large-scale time-invariant spatial uncertainty of the IGRF based on the globally averaged misfit of the model to ground-based measurements at repeat stations and observatories between 1980 and 2021. As the ground measurements are reduced to quiet-time values, the external field is minimized for the purposes of this study. We find the 68.3% confidence interval is 87 nT in the North (X) component, 73 nT in the East (Y) component and 114 nT in vertical (Z) component. Due to the Laplacian distribution of the residuals, the standard deviations are larger at 144, 136 and 293 nT, respectively. Graphical Abstract

Abstract We describe the way a global model of the geomagnetic field has been built using vector field data acquired by the absolute scalar magnetometers (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 originally affecting 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 the previous candidate IGRF 2015.0 model (being closer to the final DGRF 2015.0 model by one order of magnitude in spherical harmonic spectral terms). It is also shown to stand among the candidate 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.

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 (DGRF-2015) 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 of Terrestrial 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 individually and 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 the Gauss 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 this paper, 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 secular variation can benefit from combining physics-based core modeling with satellite observations.

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 a definitive 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 for consideration in IGRF-13. In this paper, we present the methodology used to derive our candidate models. Our candidates were built primarily from Swarm satellite data, and also relied on geomagnetic indices derived from the ground observatory network. The ground observatories played a crucial role as independent data in validating our candidates. This paper also provides a retrospective assessment of the CU/NCEI candidate model to the previous IGRF (IGRF-12) and discusses the impact of differences between candidate and final IGRF models on global model errors.

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 by comparison 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 the final 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 contribute to 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.

Abstract The International Geomagnetic Reference Field (IGRF) model is a combination of the several models developed by independent 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 obtain the 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 to 2019-Aug with a time step of 10 days and extrapolated to 01.01.2010.

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 the previous 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 harmonic coefficients for this thirteenth generation model, maps of magnetic declination, inclination and total field intensity for the epoch 2020.0, and maps of their predicted rate of change for the 2020.0 to 2025.0 time period.

Abstract We present the GFZ candidate field models for the $$13{\mathrm{th}}$$ 13 th 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 the Mag.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 the satellite 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 the geomagnetic field is the South Atlantic Anomaly, a zone of weak and decreasing field strength stretching from southern Africa over to South America. 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 western minimum 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 the core–mantle boundary, but rather to intensity changes of westward drifting flux patches contributing to the observed surface field. Also, we report a sudden change in the secular variation measured at two South Atlantic observatories around 2015.0, which occurred shortly after the well-known jerk of 2014.0.

Abstract We describe a new, original approach to the modelling of the Earth’s magnetic field. The overall objective of this study is to reliably render fast variations of the core field and its secular variation. This method combines a sequential modelling approach, a Kalman filter, and a correlation-based modelling step. Sources that most significantly contribute to the field measured at the surface 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. These errors, 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.

Abstract As 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 Swarm satellite and geomagnetic observatory ground data for the last year. In order to provide the IGRF-13 candidate, we have extrapolated the Gauss coefficients of the main field and its secular variation to January 1st, 2020. In addition, we have generated 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 classical protocols and data filters applied in geomagnetic field modelling. Novelty arrives from the application of bootstrap analysis to solve issues related to the inhomogeneity of the spatial and temporal data distributions. This new approach allows the estimation of not only the Gauss coefficients, but also their uncertainties.

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, and CHAMP 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 with respect to the deviation from a dynamo state vector at an initial condition. The data vector for the assimilation consists of the poloidal scalar potential of the geomagnetic field at the core surface and flow velocity field slightly below the core surface. Dimensionless time of numerical geodynamo is adjusted to the actual time by comparison of secular variation time scales. For SV prediction, we first generate an ensemble of dynamo simulation results from a free dynamo run. We then assimilate the ensemble to the data with a 10-year assimilation window through iterations, 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 of our 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 to 2019.50. We generate our final SV candidate model by linear fitting for the weighted sum of the ensemble MHD dynamo simulation members from 2019.50 to 2025.00. We derive errors of our SV candidate model by one standard deviation of SV histograms based on all the ensemble members.