Search

Abstract Each International Geomagnetic Reference Field (IGRF) model released under the auspices of the International Association of Geomagnetism and Aeronomy 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 a mathematical 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 the predicted 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 in the 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 to incorporate at least part of the processes responsible for short-term geomagnetic variations. In this letter, 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 that both strategies resort to “input” models of the main field and its secular variation constructed from observations. 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 of incorporating rapid physical processes into the analysis on the one hand, and the accuracy and quantification of the uncertainty impacting input models on the other hand.

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 This paper describes the design of a candidate secular variation model for the 13th generation of the International Geomagnetic Reference Field. This candidate is based upon the integration of 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 is used 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 core surface 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, and prescribed covariances for the other sources. One next considers 100 three-dimensional core states (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 for 2019.0 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 time frame and its uncertainties.

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 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 We present a new model of the geomagnetic field spanning the last 20 years and called Kalmag. Deriving from the assimilation 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 been sequentialized 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].

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.

Abstract We propose a new approach to the calculation of regular baselines at magnetic observatories. The proposed approach is based on the simultaneous analysis of the irregular absolute observations and the continuous time-series deltaF, widely used for estimating the data quality. The systematic deltaF analysis allows to take into account all available information about the operation of observatory instruments (i.e., continuous records of the field variations and its modulus) in the intervals between the times of absolute observations, as compared to the traditional baseline calculation where only spot values are considered. To establish a connection with the observed spot baseline values, we introduce a function for approximate evaluation of the intermediate baseline values. An important feature of the algorithm is its quantitative estimation of the resulting data precision and thus determination of the problematic fragments in raw data. We analyze the robustness of the algorithm operation using synthetic data sets. We also compare baselines and definitive data derived by the proposed algorithm with those derived by the traditional approach using Saint Petersburg observatory data, recorded in 2015 and accepted by INTERMAGNET. It is shown that the proposed method allows to essentially improve the resulting data quality when baseline data are not good enough. The obtained results prove that the baseline variability in time might be quite rapid.