Derivation and use of core surface flows for forecasting secular variation

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.

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.

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.

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.

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.

Antarctica is a region of great importance for studies of geomagnetism and allied fields. The present-day geometry of the Earth's main magnetic field causes the high-latitude region of the atmosphere to be directly affected by the increase in magnetospheric energy during geomagnetic storms and substorms. Intense energy input from the magnetosphere can result in visually spectacular aurora and changes in the ionosphere that affect HF (high frequency) communication. Increases in the convective electric field and auroral particle precipitation produce intense currents in the ionosphere, which are monitored through magnetic field measurements. Changes in the ionosphere are also monitored using a riometer, which measures the strength of the 30-MHz galactic radio waves that impinge on the Earth's atmosphere and thereby gives information on the changes in absorption of this signal due to changes in the ionospheric electron density. Apart from the dramatic short-term changes in the geomagnetic field recorded at Antarctica, which may be attributed to external causes, it has emerged that the Earth's complex main magnetic field, which has its origin in the fluid outer core of the Earth at a depth of about 2900 km below the surface of the Earth, is also undergoing a systematic rapid decline in the Antarctic region. The Indian Institute of Geomagnetism (IIG) started geomagnetic field measurements in Antarctica during the first Indian Antarctic Expedition in 1981–1982. With the setting up of a permanent base at Dakshin Gangotri (DG) in 1983–1984, observations were taken on a regular basis with a proton precession magnetometer (PPM), fluxgate magnetometer, and riometer. The observations were shifted to Maitri in 1990 after the DG station was abandoned, and some additional instruments were deployed at Maitri. The observations have indicated the importance of the location of Maitri, being a subauroral location during magnetically quiet periods. Thus, attributes sometimes change, however, during magnetically disturbed times when magnetospheric effects expand spatially from their quiet time locations. A large decrease in the main magnetic field observed at Maitri is now emerging as important for monitoring the evolution of reverse magnetic flux patches due to physical processes occurring in the molten iron outer core of the Earth. The present review of studies in geomagnetism and allied aspects during the past 23 Indian Antarctic expeditions summarizes the observations made during such studies and their importance.

Based on an expanded network of world magnetic observatory data, a comprehensive analysis of secular geomagnetic variations observed over a 100-year period has been carried out to determine the role of jerks in the formation of secular variations belonging to the high-frequency range of the spectrum of variations of the Earth's main magnetic field. Jerks – sharp changes in the direction of the linear trend characteristic of time series of values of secular variations of the magnetic field generated in the Earth's liquid core over decades – have been identified. Epochs of global jerks, manifesting on the scale of the entire Earth's surface with an interval of about ten years, have been identified and their spherical harmonic models have been constructed. Analysis of the morphology of the global jerk fields confirmed the idea that their source are processes occurring in the Earth's liquid core. Spectral analysis of series of secular variations, performed by the Fourier series decomposition method, made it possible to identify the main periods constituting the spectrum of secular variations with T < 10 years. Taking into account the jerk phenomena showed that all identified periods of secular variations can be interpreted within the framework of the concept of geomagnetic jerks, stochastic in the variability of manifestation both in regional and temporal aspects. Based on the analysis of the results of the conducted comprehensive research, a hypothesis is put forward that the dynamics of the Earth's main magnetic field, within centennial intervals, is formed due to the spatio-temporal superposition of global jerks caused by a sharp restructuring of the flow system on the surface of the Earth's liquid core.

<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>

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

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 great concern about the global warming observed in the troposphere has generated a large interest in the study of long-term trends in the ionosphere since the early 1990s, which has now become a significant topic in global change investigations. Some research works link ionosphere trends to anthropogenic sources such as the increase in greenhouse gas concentration, and others to natural causes such as solar and geomagnetic activity long-term changes, and secular variations in the Earth's main magnetic field. In all the cases, in order to analyze ionospheric trends, solar activity effect must be filtered out first since around 90% of ionosphere parameter variance is due to solar variations. The filtering process can generate ‘spurious’ trends in the filtered data series which may lead to erroneous conclusions. foF2 data series which include solar cycle 23 are analyzed in the present work in order to detect the effect of different filtering procedures on the determination of long-term trends. In particular, solar cycle 23 seems to have had an extreme ultraviolet (EUV) emission greater than that deduced from traditional solar EUV proxies during the maximum epoch and lower during the minimum epoch. When solar activity is filtered assessing the residuals of a linear regression between foF2 and Rz, or between foF2 and F10.7, this fact may bias trend values especially because it is at the end of the time series. The length of the period considered for trend assessment, the saturation and hysteresis effect of some ionosphere parameters, and the solar EUV proxy used are also considered in this study in order to quantify a possible spurious trend that may result as a by-product of a filtering process. Since trends expected as a consequence of anthropogenic effects are relatively small, these spurious effects may surely mask, or enhance, trends expected from anthropogenic origins.

<p><strong>Abstract:</strong></p><p>The second part of the history of the Algerian magnetic repeat station network goes back to 1989 when the new one was started with 37 stations. It was then followed by three other networks in 1993, 1997 and 2005. The first part of this history started at the beginning of the XX<sup>th</sup> and ended ca 1956.</p><p>After a 14-year break, we launched a new repeat stations network in February 2019. The number of carried out stations was increased to 51 to try to cover all the territory.</p><p>Each repeat station network consists of stations of periodically, say  5-6 years, measured of three components of the Earth's magnetic field. to try to derive the spatial distribution of the geomagnetic field of Algeria and it's secular variation. This periodicity is also very important for the need to update local as well as global geomagnetic field models such as the International Geomagnetic Reference Field (IGRF).</p><p>In this work we describe the new 2019 Algerian repeat station network. Then we will discuss the steps of the absolute measurements using two methods. The first one is called the ‘method of zero’ and the second one ‘method of residuals’. The accuracy and resolution of the instruments and data reduction used and their effect on the final results will as well be discussed. We derive the spatial distribution of the geomagnetic field, and its secular variation. Finally, we will show how local, for instance regional polynomial modeling, is the key issue.</p><p><strong>Key words</strong>: geomagnetic repeat network, absolute measurements, zero method, residual method, magnetic maps of Algeria, secular variation.</p>

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.

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.

Geomagnetic jerks are the fastest variations we observe in secular variation (SV) of the internal geomagnetic field. They have been deemed spatiotemporally unpredictable, and thus make it difficult to forecast magnetic field changes. Recent core surface flow-inversions of satellite SV data show that pulses in modelled azimuthal flow acceleration are contemporaneous with localised low latitude jerks observed in the Atlantic and Pacific from 2000—2024.In order to explore to what extent such pulses might be responsible for observed geomagnetic jerks, we simulate them with synthetic flow models. We use a Fisher–Von Mises probability distribution to spatially define the pulse, which ensures that its spherical harmonic expansion in terms of poloidal and toroidal spherical harmonic coefficients converges. To recover a dynamic flow, we add uncorrelated noise to these toroidal and poloidal acceleration coefficients. After this, we obtain SV from flow acceleration using the diffusionless induction equation, investigating a variety of background flows and core-surface magnetic field structures with our flow-acceleration pulse. Finally, we plot the expected SV at the Earth’s surface.We successfully generate geomagnetic jerks, similar to those observed by CHAMP in the Atlantic in 2003.5 and 2007, and Swarm in the Pacific in 2017 and 2020. This pulse-like simulator for low-latitude jerks is in agreement with results from numerical dynamo simulations, which suggest that jerks originate from Alfvén wave packets emitted from the inner-outer core boundary. Our results further suggest that there is no need for waves longitudinally propagating along the outer core surface for jerks to occur.