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The geomagnetic field models are presented with the external field influences taken into account. Magnetometers detect the external field, although most geomagnetic field models do not account for it. It is crucial to take into account how the external field affects the small satellite's other components. Furthermore, variations in the external field have the ability to affect the satellite's orbit and modify the spacecraft's drag, which could result in an altitude decrease and, eventually, mission failure. Consequently, to guarantee a successful mission, a comprehensive comprehension of the external field's influence on the small satellite's subsystems is required. In this work, the magnetorquers apply the magnetic control during the nanosatellite's detumbling phase. Although magnetic control cannot achieve three-axis control instantaneously, it can in near-polar trajectories due to the continuous variation of the magnetic field. In order to determine whether the geomagnetic storms may be exploited to our advantage by producing greater field variations, this study focuses on the extent to which it contributes to the magnetic control of the small satellites. [ABSTRACT FROM AUTHOR]

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.

We present a statistical study of magnetic field vector residual between Swarm observations and two Earth magnetic field models: the 13th generation International Geomagnetic Reference Field (IGRF) model and the CHAOS‐7 model. Statistics of these residuals are important for estimating potential errors for satellite operations when using Earth magnetic models as a reference, as well as for magnetosphere‐ionosphere‐thermosphere studies examining energy input into the system. Magnetic field residuals are calculated as vector differences between observations and model estimation at Swarm satellite positions from 2014 to 2020. Magnetic field residuals for both models increase as geomagnetic activity level increases, and the largest magnitude of vector difference can be around 1800 nT with relatively small angle differences. The CHAOS‐7 model shows lower magnetic field residuals compared to IGRF‐13. North‐south hemispheric asymmetries are seen in magnetic field residuals for high Kp values larger than 6 with the southern hemisphere (SH) having more frequent occurrence of magnetic field residuals larger than 300 nT, especially during SH summer. Most large residual values appear in the high‐latitude region with SH seeing additional large residuals around the South Atlantic Anomaly region. Midnight and noon sectors show the strongest interhemispheric asymmetries. The northern hemisphere shows more frequent occurrence of large residuals above 75° magnetic latitude throughout all local times compared to the SH. Identifying asymmetries in large magnetic residuals under high geomagnetic activity levels is helpful for studying the difference in response to ionospheric disturbances in the two hemispheres. Key Points: Comparison between Swarm magnetic field vector observations and Earth magnetic field modelsStatistical magnetic field residual maps show largest differences in high latitude region and around the South Atlantic AnomalyMore frequent occurrence of large magnetic field residual under high geomagnetic activity levels in southern hemisphere [ABSTRACT FROM AUTHOR]

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.

Aeromagnetic surveys play an important role in many fields, for example, archaeology, anti-submarine warfare, and geophysical exploration. Being in the geomagnetic field, the aircraft generates a great deal of magnetic interference, resulting in bad performance during detection surveys. Thus, it is necessary and important to perform aeromagnetic compensation in advance. Conventional aeromagnetic compensation methods consider that the geomagnetic gradient is approximately zero after bandpass filtering, bringing about the inaccuracy of compensation coefficients. To address this issue, an improved aeromagnetic compensation method robust to geomagnetic gradient is proposed. In this study, the International Geomagnetic Reference Field (IGRF) model was employed to model the geomagnetic gradient. Then, the estimated geomagnetic gradient was subtracted from the measured data, which improved the accuracy of the compensation equations. Field experiments were conducted to verify the effectiveness of the proposed method. The experimental results show that compared to the traditional method, the compensation performance of the proposed method was improved by 152% to 329%. For the level flight, the standard deviation of residual noise after compensation can be as low as 3.3pT. The results indicate that the proposed method can significantly improve the compensation effect, showing great benefits for weak magnetic anomaly detection. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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.

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 FROM AUTHOR]

This study investigates the effects of magnetic disturbances resulting from geospace storms on the satellite attitudes estimated by EKF. It is shown that the increasing levels of geomagnetic activity affect geomagnetic field vectors predicted by IGRF and T89 models. Various sensor combinations including magnetometer, gyroscope, and sun sensor are evaluated for magnetically quiet and active conditions. Errors are calculated for estimated attitude angles and differences were discussed. This study emphasizes on the importance of environmental factors on the satellite attitude determination systems. • Focuses on using an empirical model for global magnetosphere in attitude estimation. • Estimates the attitude angles with smaller errors when using T89 during active days. • Emphasizes on the effects of the geomagnetic disturbances on the attitude angles. • Helps to choose sensor combination during quiet/disturbed times for better attitude. [ABSTRACT FROM AUTHOR]

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 FROM AUTHOR]

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 FROM AUTHOR]

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 FROM AUTHOR]

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 FROM AUTHOR]

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 FROM AUTHOR]

We present the GFZ candidate field models for the 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 FROM AUTHOR]

Aeromagnetic surveys play an important role in many fields, for example, archaeology, anti-submarine warfare, and geophysical exploration. Being in the geomagnetic field, the aircraft generates a great deal of magnetic interference, resulting in bad performance during detection surveys. Thus, it is necessary and important to perform aeromagnetic compensation in advance. Conventional aeromagnetic compensation methods consider that the geomagnetic gradient is approximately zero after bandpass filtering, bringing about the inaccuracy of compensation coefficients. To address this issue, an improved aeromagnetic compensation method robust to geomagnetic gradient is proposed. In this study, the International Geomagnetic Reference Field (IGRF) model was employed to model the geomagnetic gradient. Then, the estimated geomagnetic gradient was subtracted from the measured data, which improved the accuracy of the compensation equations. Field experiments were conducted to verify the effectiveness of the proposed method. The experimental results show that compared to the traditional method, the compensation performance of the proposed method was improved by 152% to 329%. For the level flight, the standard deviation of residual noise after compensation can be as low as 3.3pT. The results indicate that the proposed method can significantly improve the compensation effect, showing great benefits for weak magnetic anomaly detection.

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 FROM AUTHOR]

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 FROM AUTHOR]

A surprisingly fast secular drift of the Northern geomagnetic dip pole during the last two decades has attracted much interest lately, in particular, evoking speculations about a possibility of a sweeping relocation of the auroral oval. This letter presents first results of a model investigation of this issue, based on an empirical representation of the distant magnetosphere combined with a series of internal geomagnetic field models for 12 epochs, covering the interval from 1965 to 2020. The secular drift of the northern auroral oval was found to result in its net displacement over the 55‐year period, commensurate with the concurrent shifts of the centered, eccentric, and corrected geomagnetic poles, all of them much smaller than the enormous spurt of the northern dip pole. In the Southern Hemisphere, the shift of the auroral oval and of the poles over the same period is much weaker, revealing a remarkable interhemispheric asymmetry. Plain Language Summary: The auroral displays associated with space storms occur within two band‐like regions, encircling north and south polar caps and called auroral ovals. Aside from highly dynamical reconfigurations of the ovals during space weather events, there exists a much slower and steady shift of their position, associated with a gradual change of the geomagnetic field, termed secular variations and closely related to slow relocation of the geomagnetic poles over the Earth's surface. A remarkable phenomenon observed during the last few decades is an unusually fast shift of the geomagnetic dip pole (a point with strictly vertical field direction) from North Canada toward East Siberia. A natural question is then: how large is the secular shift of the auroral ovals in comparison with the fast relocation of the dip pole? In this work, the problem is addressed from the viewpoint of a magnetospheric model based on spacecraft data. It is shown that the secular shift of the auroral oval between 1965 and 2020 is about the same as that of the geomagnetic dipole axis, which is much slower than the fastly racing dip pole. In the Southern Hemisphere, the oval shifts are much smaller than in the Northern Hemisphere. Key Points: From 1965 to 2020 the Northern auroral oval drifted by 4‐5 degrees of latitude, comparable with centered, eccentric, and corrected pole shiftsThe 15‐degree jump of the Northern dip pole over the same period is irrelevant to the auroral oval shift and is a largely geometric effectSouthern oval shift over the same period, its shape, and pole behavior are drastically asymmetric to those in the Northern Hemisphere [ABSTRACT FROM AUTHOR]

Abstract: In the presence of drift‐shell splitting intrinsic to the International Geomagnetic Reference Field magnetic field model, pitch angle scattering from Coulomb collisions experienced by radiation‐belt electrons in the upper atmosphere and ionosphere produces extra radial diffusion, a form of neoclassical diffusion. The strength of the neoclassical radial diffusion at L < 1.2 exceeds that expected there from radial‐diffusion mechanisms traditionally considered and decreases with increasing L‐shell. In this work we construct a numerical model for this coupled (radial and pitch angle) collisional diffusion process and apply it to simulate raw count‐rate data observed aboard the Gemini spacecraft for several years after the 1962 Starfish nuclear detonation. The data show apparent lifetimes 10–100 times as long as would have been expected from collisional pitch angle diffusion and Coulomb drag alone. Our model reproduces apparent lifetimes for >0.5‐MeV electrons in the region 1.14 < L < 1.26 to within a factor of 2 (comparable to the uncertainty quoted for the observations). We conclude that neoclassical radial diffusion (resulting from drift‐shell splitting intrinsic to International Geomagnetic Reference Field's azimuthal asymmetries) mitigates the decay expected from collisional pitch angle diffusion and inelastic energy loss alone and thus contributes importantly to the long apparent lifetimes observed at these low L‐shells. [ABSTRACT FROM AUTHOR]

This paper implements an open-loop controller for generating earth’s magnetic field in vessel’s co-ordinate frame. It also incorporates the rotational movements along the three axes, without physically moving the object. This has potential application in prediction of signature for ferromagnetic marine vessels in changing earth’s magnetic field experienced by the vessel due to change in location. It also considers the effect of roll, pitch and heading changes. Uniform magnetic field simulator is designed to generate the required magnetic field in the vessel’s coordinate frame. Simulation results are verified using experimental laboratory setup. [ABSTRACT FROM AUTHOR]

We use Open Geospace General Circulation Model (OpenGGCM) simulations to predict magnetic field perturbations at Low Earth Orbiting (LEO) satellites such as Swarm, at high latitudes. The simulations allow us to separate three different major contributions to the observed perturbations, i.e., the perturbations caused by currents in the outer magnetosphere, field-aligned currents (FACs), and the currents flowing in the ionosphere. We find that at an altitude of 500 km the strongest contribution comes from FACs, followed by the perturbations caused by the ionospheric currents, while the magnetospheric currents make only a minor contribution. The high latitude perturbations do not average out over extended quiet time periods. There are significant variations in the patterns; however, on a large scale, the basic shape of the pattern remains stable. Thus, without explicitly removing the perturbations from the data, any spherical harmonics fit is expected to incur a bias. Although the predicted OpenGGCM perturbations do not compare particularly well with Swarm data, the simulations reproduce the overall pattern. However, they may still be useful to reduce the bias of the ensemble and produce better global spherical harmonic fits, by producing an ensemble whose external field contributions average out. Since this paper only scratches the surface of the role that models of the external field can play in producing unbiased internal field models, much progress is still possible, for example by improving the external model, investigating larger ensembles, and by considering data from geomagnetically disturbed times. [ABSTRACT FROM AUTHOR]

Inertial navigation system has drift error in underwater applications. Use of DVL with Kalman filter for position and attitude correction is common. Using velocity data decreases drift error in position estimation but this error exists and increases linearity with time. In this article the navigation system consists of inertial measurement unit (IMU) and a Doppler velocity log (DVL) along with depth sensor. With use of magnetic field measurement and earth magnetic field map a new measurement is generated. Discrete extended Kalman filter with indirect feedback is used for tightly coupled integrated navigation algorithm. This algorithm is based on inertial navigation error dynamics. This paper demonstrates the effectiveness of algorithm through simulation. The procedure of simulation is done by sensor data generation. Arbitrary trajectory with specific kinematic characteristic (linear and angular velocity and acceleration) is generated. Sensor data by adding noise and bias to kinematic characteristic of trajectory is produced. Simulation results reveal that the new algorithm with use of magnetic data and earth magnetic field map decreases the drift error with comparison to conventional INS-DVL integrated navigation algorithm. [ABSTRACT FROM AUTHOR]

The nanosatellite POPSAT-HIP1 is a Cubesat-class spacecraft launched on the 19th of June 2014 to test cold-gas based micro-thrusters; it is, as of April 2015, in a low Earth orbit at around 600 km of altitude and is equipped, notably, with a magnetometer. In order to increment the performance of the attitude control of nanosatellites like POPSAT, it is extremely useful to determine the main biases that act on the magnetometer while in orbit, for example those generated by the residual magnetic moment of the satellite itself and those originating from the transmitter. Thus, we present a methodology to perform an in-orbit offline estimation of the magnetometer bias caused by the residual magnetic moment of the satellite (we refer to this as the residual magnetic dipole bias, or RMDB). The method is based on a genetic algorithm coupled with a simplex algorithm, and provides the bias RMDB vector as output, requiring solely the magnetometer readings. This is exploited to compute the transmitter magnetic dipole bias (TMDB), by comparing the computed RMDB with the transmitter operating and idling. An experimental investigation is carried out by acquiring the magnetometer outputs in different phases of the spacecraft life (stabilized, maneuvering, free tumble). Results show remarkable accuracy with an RMDB orientation error between 3.6 ° and 6.2 ° , and a module error around 7 % . TMDB values show similar coherence values. Finally, we note some drawbacks of the methodologies, as well as some possible improvements, e.g. precise transmitter operations logging. In general, however, the methodology proves to be quite effective even with sparse and noisy data, and promises to be incisive in the improvement of attitude control systems. [ABSTRACT FROM AUTHOR]

En los relevamientos magnéticos realizados sobre la superficie de la Tierra se utiliza el Campo Geomagnético Internacional de Referencia (IGRF) para sustraer la contribución del campo principal de la Tierra. Cada cinco años se publica un nuevo modelo de IGRF y la variación secular del período previo debe ser actualizada, generándose el denominado modelo DGRF. Una vez que el DGRF es publicado, las anomalías magnéticas calculadas previamente deben ser recalculadas. La actualización de las anomalías podría ser particularmente importante para relevamientos magnéticos regionales o para compilaciones de datos magnéticos adquiridos en diferentes épocas. En este trabajo se muestra la importancia de esta corrección, particularmente para el periodo 1995-2000, en el cual la diferencia DGRF-IGRF es llamativamente apreciable. Se documenta la validez de la corrección utilizando datos del Observatorio Geomagnético Permanente de Trelew, Argentina. doi: https://doi.org/10.22201/igeof.00167169p.2003.42.4.317

Every five years a new International Geomagnetic Reference Field (IGRF) model is released and the secular variation for the previous period is updated, producing the definitive DGRF model. Once a DGRF is released, the previously calculated magnetic anomalies are updated. We show the importance of this correction for the 1995-2000 period, in which the DGRF-IGRF difference is anomalously large. We document the validity of the correction by using data from the permanent geomagnetic Observatory of Trelew, Argentina.

The solar wind contributes to the formation of unique space environment called the Earth's magnetosphere by various interactions with the Earth's magnetic field. Thus the solar-terrestrial environment affects the Earth's magnetic field, which can be observed with an instrument for the magnetic field measurement, the magnetometer usually mounted on the rocket and the satellite and based on the ground observatory. The magnetometer is a useful instrument for the spacecraft attitude control as well as the Earth's magnetic field measurements for a scientific purpose. In this paper, we present the preliminary design and test results of the two onboard magnetometers of KARI's (Korea Aerospace Research Institute) sounding rocket, KSR-3, which will be launched four times during the period of 2001-02. The KSR-3 magnetometers consist of the fluxgate magnetometer, MAG/AIM (Attitude Information Magnetometer) for acquiring the rocket flight attitude information, and of the search-coil magnetometer, MAG/SIM (Scientific Investigation Magnetometer) for the observation of the Earth's magnetic field fluctuations. With the MAG/AIM, the 3-axis attitude information can be acquired by the comparison of the resulting dc magnetic vector field with the IGRF (International Geomagnetic Reference Field). The Earth's magnetic field fluctuations ranging from 10 to 1,000 Hz can also be observed with the MAG/SIM measurement.

It is a well known fact that ionospheric delay error is a predominant factor which influences the positioning accuarcy of GNSS. Although the main part of the first-order ionospheric delay error can be removed by the frequency-dependent behaviors of the ionosphere, the second-order ionospheric delay error must be eliminated to achieve millimetre-scale positioning accuracy. Due to COSMIC occultation providing electron density profiles on the global scale, the paper presents the first-order and the second-order ionospheric delay error analysis on the global scale using the inversion of electron density profiles from COSMIC occultation data during 2009-2011. Firstly, because of the special geographical location of three ISR (incoherent scatter radar), the first-order and the second-order ionospheric delay errors are calculated and discussed; the paper also shows and analyzes the diurnal, seasonal, semi-annual variation of ionospheric delay error with respect to signal direction. Results show that for the L1 signal path, the first-order ionospheric delay error is the largest near the equator, which is circa 7 m; the maximum second-order ionospheric delay error are circa 0.6 cm, 0.8 cm and 0.6 cm respectively for L1 signals coming from the zenith, the north and the south at 10 degree elevation angles. The second-order ionospheric delay error on the L1 signal path from zenith are the symmetry between 15° and ∼15° with respect to magnetic equator, and are nearly zero at the magnetic equator. For the first time, the second-order ionospheric delay error on the global scale is presented, so this research will greatly contribute to analysing the higher-order ionospheric delay error characteristics on the global scale. [ABSTRACT FROM AUTHOR]