Candidate geomagnetic field models for IGRF-14 and secular acceleration since 2020

Geomagnetic field data from four observatories and annual field surveys between 2005 and 2015 provide a detailed description of Earth’s magnetic field changes over South Africa, Namibia and Botswana on time scales of less than 1 year. The southern African area is characterized by rapid changes in the secular variation pattern and lies in close proximity to the South Atlantic Anomaly (SAA) where the geomagnetic field intensity is almost 30 % weaker than in other regions at similar latitudes around the globe. Several geomagnetic secular acceleration (SA) pulses (geomagnetic jerks) around 2007, 2010 and 2012 could be identified over the last decade in southern Africa. We present a new regional field model for declination and horizontal and vertical intensity over southern Africa (Southern African REGional (SAREG)) which is based on field survey and observatory data and covering the time interval from 2005 to 2014, i.e. including the period between 2010 and 2013 when no low Earth-orbiting vector field satellite data are available. A comparative evaluation between SAREG and global field models like CHAOS-5, the CHAMP, Orsted and SAC-C model of the Earth's magnetic field and International Geomagnetic Reference Field (IGRF-12) reveals that a simple regional field model based on a relatively dense ground network is able to provide a realistic representation of the geomagnetic field in this area. We particularly note that a global field model like CHAOS-5 does not always indicate similar short-period patterns in the field components as revealed by observatory data, while representing the general secular variation reasonably well during the time interval without near-Earth satellite vector field data. This investigation further shows the inhomogeneous occurrence and distribution of secular variation impulses in the different geomagnetic field components and at different locations in southern African.

The International Geomagnetic Reference Field (IGRF) 10th Generation was adopted in 2004 by the International Association of Geomagnetism and Aeronomy (IAGA) Working Group V-MOD. It is the latest version of a standard mathematical description of the Earth’s main magnetic field and is used widely in studies of the Earth’s deep interior, its crust and its ionosphere and magnetosphere. This generation differs from the previous generation with the replacement of the secular-variation model for 2000.0–2005.0 with a main-field model at 2005.0 and a secular-variation model for 2005.0–2010.0. The IGRF is the product of a huge collaborative effort between magnetic field modellers and the institutes involved in collecting and disseminating magnetic field data from satellites and from observatories and surveys around the world. This paper lists the new coefficients and includes contour maps and pole positions.

The International Geomagnetic Reference Field (IGRF) is a series of mathematical models of the main geomagnetic field and its secular variation. Each model consists of a set of spherical harmonic (or Gauss) coefficients, g and h in a series expansion of the geomagnetic potential [Formula: see text], where a is the mean radius of the Earth (6371.2 km); r the radial distance from the center of the Earth; ϕ the east longitude measured from Greenwich; θ the geocentric colatitude; and [Formula: see text] the associated Legendre function of degree n and order m, normalized according to the convention of Schmidt [see, e.g., Langel (1987)]. In principle, N should be ∞ but the Working Group is of the opinion that in practice the available data for most epochs do not justify N greater than 10. This value is chosen to maintain consistency between models at different epochs. The coefficients are in units of nanotesla (nT).

Improving forecasts of the temporal and spatial changes of the Earth's main magnetic field over periods of less than 5 years has important scientific and economic benefits. Various methods for forecasting the rate of change, or secular variation, have been tried over the past few decades, ranging from the extrapolation of trends in ground observatory measurements to computational geodynamo modeling with data assimilation from historical magnetic field models. We examine the utility of an intermediate approach, using temporally varying core surface flow models derived from relatively short periods of magnetic field data to produce, by advection, secular variation estimates valid for the Earth's surface. We describe a new method to compute a core flow changing linearly with time from magnetic secular variation and acceleration data. We invert a combination of data from the CHAMP satellite mission and ground observatories over the period 2001.0 to 2010.0 for a series of such models. We assess their ability to forecast magnetic field changes by comparing them to CHAOS‐4, a state‐of‐the‐art model using data from 1997 to 2014.5. We show that the magnetic field predictions tend to have a lower root‐mean‐square difference from CHAOS‐4 than the International Geomagnetic Reference Field or World Magnetic Map series of secular variation models.

IGRF (International Geomagnetic Reference Field) are the models of geomagnetic main field and secular variation. The IGRF errors are from the neglecting external field, the truncation of the spherical harmonic progress, the asymmetry of the observatory distribution, the measure, and the neglecting of the crust geomagnetic anomalies. Analyzing the IGRF error at China continent region can be propitious to our investigation using the IGRF data. If Beijing observatory at which there are same great disturbs and same geomagnetic anomaly is excluded, the IGRF root‐mean‐square error of the other 29 main observatories is 146.9nT.

The global main magnetic field model describes the space-time distribution characteristics of the main magnetic field. The order of the main magnetic field in the model is one of the key issues to build the main magnetic field model. This paper used Bayesian inference to analyze the global geomagnetic main field model and compares model orders based on Bayesian evidence. It provided a statistical perspective for the main field order selection. Using magnetic observations from Swarm satellites, the evidence for different orders of the main field model was estimated. The results show that order <italic>N</italic> = 12 has the global best evidence in model from 1 to 20. Referring to the threshold interval given by Jefrrey’s scale, the data preference for order <italic>N</italic> = 12 is significantly better than other orders. The experiment shows that the evidence reasoning of the main magnetic field order can be used to study the main magnetic field contribution, and the results match the power spectrum analysis of spherical harmonic of order <italic>N</italic> = 14.

In August 1981 the International Association of Geomagnetism and Aeronomy revised the International Geomagnetic Reference Field (IGRF). It is the second revision since the inception of the IGRF in 1968. The revision extends the earlier series of IGRF models from 1980 to 1985, introduces a new series of definitive models for 1965-1975, and defines a provisional reference field for 1975-1980. The revision consists of: (1) a model of the main geomagnetic field at 1980.0, not continuous with the earlier series of IGRF models, together with a forecast model of the secular variation of the main field during 1980-1985; (2) definitive models of the main field at 1965.0, 1970.0, and 1975.0, with linear interpolation of the model coefficients specified for intervening dates; and (3) a provisional reference field for 1975-1980, defined as the linear interpolation of the 1975 and 1980 main-field models. The new models are series of solid spherical harmonics up to and including the tenth degree and order for the main-field models, and up to and including the eighth degree and order for the secular variation model. The models were derived from three sets of proposed models by taking weighted means. The weights were chosen according to the apparent accuracy of the proposed models. A brief history of the IGRF, a review of basic formulas, and a set of world contour maps of the geomagnetic elements based on the IGRF 1980 model are included.

The International Association of Geomagnetism and Aeronomy (IAGA) Division I, Working Group 1, deals with the topic “Analysis of the Main Field and Secular Variations.” One of the more important functions of the working group is the periodic revision of the International Geomagnetic Reference Field (IGRF). The 13 members of the working group have professional interests covering a broad spectrum of geomagnetic science, including the theory and practice of geomagnetic analysis and modeling, the theory of the origin of the magnetic fields of the earth and other bodies, the theory of geomagnetic secular variation, the application of field models in magnetic survey data processing, and geomagnetic charting.

The International Geomagnetic Reference Field (IGRF) model is a series of models that describe the large scale magnetic field measured at the Earth's surface. It is used by a wide range of scientists and industries, including in navigation, space weather applications, and resource exploration. The 14th generation, IGRF-14, is the result of an international collaboration over 19 different lead research groups. This new generation provides a definitive model of the main magnetic field (MF) for the epoch 2020.0, a prediction of the MF for 2025.0, and a predicted average annual time variation of the magnetic field for 2025.0 2030.0. The first time derivative of the magnetic field, known as secular variation, (SV) is linked to the flow at the top of Earth's outer core. As such, the ensemble of IGRF-14 candidate models can be used to investigate predicted core flow variability between 2020.0 and 2030.0. We use the pygeodyn Python package using the AR-1 'dense' methodology, the 71% geodynamo prior, and keep all inversion parameters fixed to ensure that differences in inferred flow arise solely from variations from the IGRF candidate models. Our results demonstrate that while all candidates produce broadly similar flow spectra for all degrees, candidates that deviate most from the median IGRF model also show the largest differences in flow. In all cases, the flow speed difference remains below 25% of the maximum flow speed of the Huber-weighted mean model in space, with most discrepancies occurring at small spatial scales. The greatest flow uncertainty appears over the Pacific and in the polar regions, where constraints are weaker. Finally, we assess the impact of the maximum spherical harmonic degree truncation of the SV candidate models by comparing two SV candidates truncated at spherical harmonic degree 13 instead of 8. Increasing the truncation degree of SV alters the flow spectral energy at all degrees and increases the maximum flow speed by up to 31%, despite the flow maps remaining highly correlated. This study supports the idea of raising the spherical harmonic truncation degree to 13 for the SV predictioncomponent of theIGRF.

In the present paper we discuss a few issues regarding the secular variation (SV) and secular acceleration (SA) of the geomagnetic field that have consequences on mapping them at regional scales. Data from the European network of geomagnetic observatories have been analyzed from the perspective offered by existing long time series of annual means. The existence of high-frequency ingredients in the temporal change of the main field has been taken into account too. The importance of eliminating, from observatory and main field model data, prior to any discussion on secular variation, the signal related to external variations is demonstrated. Its consequences for SV analysis and/or mapping, including the jerk concept, are shown. Also, the importance of the geographical scale at which the SV is represented is discussed. To that aim, we used gufm1, IGRF and CM4 models for the main field from which the residual external signature was eliminated. The contribution of high-frequency ingredients to the map pattern is revealed. The results of the paper set additional observational constraints to the main field and geodynamo modeling.

A seventh-generation revision of the International Geomagnetic Reference Field (IGRF) was adopted by the International Association of Geomagnetism and Aeronomy (IAGA) at the XXI General Assembly of the International Union of Geodesy and Geophysics in July 1995. The new spherical harmonic models adopted are based on weighted averages of candidate models submitted by NASA's Goddard Space Flight Center, the Russian Institute of Terrestrial Magnetism, Ionospheric, and Radio Wave Propagation-IZMIRAN, and jointly by the US Naval Oceanographic Office and the British Geological Survey. The revised IGRF specifies the Earth's main field from 1900 to 2000 and is declared to be definitive from 1945 to 1990. This paper lists the IGRF coefficients, describes the derivation of the new IGRF models, and examines aspects of the IGRF's accuracy, continuity, and behaviour during this century.

Simple additional constraints on regional models of the geomagnetic secular variation field

The International Geomagnetic Reference Field (IGRF) has been regularly updated since its inception in 1965. Every recent iteration contains an estimate of the geomagnetic secular variation (SV), for the intermediate years between iterations. We submit a candidate model for the geomagnetic secular variation (SV) for the period 2025–2030 for the 14th generation of the IGRF. Given the recent evidence in the geomagnetic SV record for core surface waves, we forecast SV based on the periodic behaviour of core surface flow acceleration. We obtain an advective core surface flow model, in terms of poloidal and toroidal flow coefficients, from spatial gradients of SV geomagnetic virtual observatory data from the low-Earth orbiting CHAMP and Swarm missions from January 2001 to January 2010, and April 2014 to January 2024, respectively. From these, we calculate the flow acceleration coefficients from the first time-derivative. This assumes the flow is spatio-temporally simple, without imposing any physical constraints on its geometry. We fit each acceleration coefficient with a sinusoidal function, which is used to extrapolate 6 years into the future. These sinusoidally varying acceleration time series are integrated over time to obtain the core flow coefficients, which are then used to predict the average advected SV over the 5-year IGRF period. We recreate previous IGRF predictions using our CHAMP-based flows to validate our methodology, which we find to outperform previous IGRF iterations, and use the Swarm-based flows to forecast the SV for IGRF-14. Our Swarm-based model predicts sudden changes in SV—also known as geomagnetic jerks—in 2024 in the Equatorial Pacific, and in 2028 in the region around central Africa. Although the IGRF SV is a snapshot over a 5-year period, allowing for periodic behaviour offers potential improvements over other methods of prediction.Graphical Supplementary InformationThe online version contains supplementary material available at 10.1186/s40623-025-02347-x.

Investigating the 2003 geomagnetic jerk by simultaneous inversion of the secular variation and acceleration for both the core flow and its acceleration

&amp;lt;p&amp;gt;2020 marks the start of a new 5-year cycle and updated releases of the World Magnetic Model (WMM) and International Geomagnetic Reference Field (IGRF). These models provide a reference for the up-to-date internal geomagnetic field in 2020, and a prediction of its secular variation for the next 5&amp;amp;#160;years, to 2025. While similar in some aspects, the two models have different specifications and many different users across diverse fields. They provide references to be used primarily for navigation (WMM) and geomagnetic coordinate systems (IGRF).&amp;lt;/p&amp;gt;&amp;lt;p&amp;gt;BGS produces the WMM in collaboration with the US&amp;amp;#8217; NOAA/NCEI, while the IGRF is produced by an IAGA Div. V-MOD task force, this time consisting of fifteen teams across nine nations, including BGS. Here we present a summary of the production of the updated WMM2020 and IGRF-13, and BGS efforts to enable access to these models.&amp;lt;/p&amp;gt;&amp;lt;p&amp;gt;We also present a retrospective analysis of the predictive components of the candidate models for previous IGRF epoch&amp;amp;#8217;s secular variation. Recent epochs have seen notable geomagnetic jerks and the acceleration of the North magnetic dip pole, features not well represented by the constant SV format of models such as the IGRF. We assess the range of candidate models submitted for previous IGRF epochs, assess the accuracy of physically derived predictions versus mathematical extrapolations, and discuss the implications given the range of candidate models submitted for IGRF-13 secular variation over the next five years.&amp;lt;/p&amp;gt;