International geomagnetic reference field: The third generation.

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 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).

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.

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.

Secular variation of the Earth's main magnetic field is believed to originate in the Earth's core. (The main field is operationally defined as comprising spherical harmonics of degree l⩽10.) I propose a different mechanism of secular variation: ocean water being a conductor of electricity, the magnetic field induced by the ocean as it flows through the Earth's main field may depend on time and manifest itself globally as secular variation. This proposal is supported by calculation of secular variation using the induction equation of magnetohydrodynamics, the observed main field and the ocean flow field. The predicted secular variation is in rough agreement with that observed. Additional support is provided by the striking temporal correlation (hitherto unsuspected) between the intensity of the North Atlantic oceanic circulation and the rate of secular variation in Western Europe; this explains, in particular, the geomagnetic jerks, and the recently discovered correlation between secular variation and climate. Spatial correlation between ocean currents and secular variation is also strong.

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.

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, the g's and h's in a series expansion of the following geomagnetic potential.

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.

IGRF-14 is the fourteenth generation of the International Geomagnetic Reference Field (IGRF), a spherical harmonic model of Earth’s main magnetic field and its secular variation, developed through international collaboration under the auspices of the International Association of Geomagnetism and Aeronomy (IAGA). This paper describes the development, in October 2024, of candidate main field (MF) models at epochs 2020.0 and 2025.0, and a secular variation (SV) model at 2025.0, derived from Swarm satellite data, as well as the validation of the SV model using ground-based observatory measurements. Swarm data collected through May 2025 were subsequently used to update the continuous parent model from which these candidates were derived, which now spans 2014.42 to 2024.92. This model is used to conduct a retrospective assessment of SV performance and to analyze recent secular acceleration (SA) signals. Our results reveal a pronounced SA pulse centered in 2022 and provide evidence for a geomagnetic jerk in 2024, confirmed by recent observatory data from Western Europe and North America. These rapid, nonlinear core field changes have already contributed to the early degradation of the IGRF-14 SV forecast, underscoring the challenges of modeling geomagnetic field evolution and the importance of continuous satellite and ground-based observations. Graphical Abstract

<p>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 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).</p><p>BGS produces the WMM in collaboration with the US’ 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.</p><p>We also present a retrospective analysis of the predictive components of the candidate models for previous IGRF epoch’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.</p>

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.

Test of IGRF (1980) main field and secular variation in Europe

SUMMARY In this pilot study we describe a method for extracting the secular variation constituent of the Earth’s magnetic field from underway shipboard total intensity magnetic measurements. From a large amount of shipboard data obtained in the NE Atlantic, during the period 1956 to 1988, some 29 000 secular variation values were calculated at cross-over points. These results are then compared with those obtained from the International Geomagnetic Reference Fields (IGRF) in this region. Statistical analysis reveals that the ‘shipboard’ values are able to match, and marginally improve upon the IGRF values across the oceans, so long as the determination is made from a sufficiently large data set of observed values. This method thus enables the additional utilization of marine observations in the analysis of secular variation patterns across the oceans, which could lead to a more detailed view of these patterns than has been available before.

On the basis of the magnetic survey data during 1998-2001, the China Geomagnetic Reference Field Secular Variation model for 2000, CGRF-SV2000, is established. The model shows a slow and smooth variation of the magnetic field in China area. The unsigned average annual rates are 12.2nT/a, 8.2nT/a, 43.8nT/a, 11.8nT/a, 0.96'/a, 2.99'/a and 22.4nT/a for seven elements X,Y,Z,H,D,I and F, respectively. These rates are less than the global rates of IGRF by 1/3 to 1/2. The variations of different elements show an unified SV pattern in China: the north geomagnetic pole is moving to China, or China is moving toward high latitude at a rate 3'/a. In addition, the variation of declination D shows that the contrast of D between Eastern and Western China is enhanced. As a comparison and test, the 8-th generation of the International Geomagnetic Reference Field (IGRF) models is analyzed. The global SV estimated by IGRF models shows similar characteristics compared with CGRF-SV2000, although the annual rates of IGRF-SV are greater than those of CGRF-SV, and some regional (or local) anomalies are noted.

A best current model of the main geomagnetic field is presented as a response to a need for an “International Geomagnetic Reference Field”. This model is described by a series of 120 spherical harmonic coefficients and their first and second time derivatives from an epoch 1960.0. It was derived from a sample of all magnetic survey data available from the interval 1900-1964 plus a recent global distribution of preliminary total field observations from the OGO-2 (1965-81A) spacecraft for epoch 1965.8. A duplicate data selection was made and the resulting field model compared with the first to help evaluate the minimum error. It was noted that the root —mean—square difference between the two models was about 30γ in the force components, 0.04 degrees in dip and 0.3 degrees in declination at the earth's surface for 1965.0.