Estimating error associated with a magnetic field model

A common requirement for users of magnetic field models is to have information about the accuracy of the model. Any signal not captured by the model is part of the error, for example the unmodelled crustal and external fields. Some models are used long after they have been produced and errors associated with prediction of the core field inevitably arise. Estimates of ground-based errors were derived as part of the recent World Magnetic Model production. These estimates were derived from vector data from observatories and repeat stations around the world combined with scalar data from marine and airborne surveys. The errors arising from the crustal and external fields have distinct spatial patterns, with local maxima in the auroral and polar regions for the external field. Declination, the element of the magnetic field of greatest interest to many users, is not linear in spherical harmonic model coefficients but can be propagated from the orthogonal components which are linear. This results in further spatial variations (inclination and horizontal and total intensities are also affected). Some of these propagation-related spatial variations are difficult to validate in ground-based measurements because of the poor spatial coverage. We investigate whether satellite data such as those from the Swarm mission can provide such validation. To derive all-inclusive error estimates for a particular magnetic field model, the errors from the crustal and external fields and core field prediction can be combined with the propagated error estimates

State of the geomagnetic field

The performance of the World Magnetic Model 2020 (WMM2020) was assessed by comparing its predictions at 2022.0 with that of a more recent model inferred from data collected by the European Space Agency Swarm satellites until September 2021. For all magnetic field components, the WMM2020 global root-mean-square error increased by less than 1.5% over the past two years and remained well below the maximum error allowed by the U.S. Department of Defense WMM specification. In addition, the WMM2020 secular variation was found to still be a very good approximation of the actual secular variation observed at ground-based observatories and Swarm-based geomagnetic virtual observatories in 2021. This suggests that nonlinear changes in the Earth’s magnetic field remained small over the past two years. Since 2020, the north (respectively south) magnetic dip pole has moved at an average speed of 44 km/yr (respectively 9 km/yr) without any noticeable change in direction. These movements led to minor changes in the shape and location of the WMM blackout zones, where compass accuracy is degraded. The South Atlantic Anomaly, where the geomagnetic field intensity is smallest, continued to deepen (by about 50 nT at sea level) and to move westwards (its center moved by about 50 km at sea level)

The US/UK World Magnetic Model for 2015-2020

This report contains a complete description of the World Magnetic Model (WMM) 2015. Section 1 contains information that users of WMM2015 require in order to implement the model and software in navigation and heading systems, and to understand magnetic charts, poles and geomagnetic coordinate systems. Section 2 contains a detailed summary of the data used and the modeling techniques employed. Section 3 contains an assessment of the model uncertainties and a description of the error model provided with the WMM2015. Section 4 contains charts of all the magnetic elements at 2015.0 and their expected annual rates of change between 2015.0 and 2020.0. These predicted changes are based upon the best knowledge of the geomagnetic main field evolution at the time the WMM was released. Sponsored by the U.S. National Geospatial-Intelligence Agency (NGA) and the U.K. Defence Geographic Centre (DGC), the World Magnetic Model (WMM) is produced by the U.S. National Oceanic and Atmospheric Administration’s National Geophysical Data Center (NOAA/NGDC) and the British Geological Survey (BGS). It is the standard model used by the U.S. Department of Defense (DoD), the U.K. Ministry of Defence, the North Atlantic Treaty Organization (NATO) and the International Hydrographic Organization (IHO), for navigation, attitude and heading referencing systems using the geomagnetic field. It is also used widely in civilian navigation and heading systems

The US/UK World Magnetic Model for 2020-2025

This report contains a complete description of the World Magnetic Model (WMM) 2020. Section 1 contains information that users of WMM2020 require in order to implement the model and software in navigation and heading systems, and to understand magnetic charts, poles and geomagnetic coordinate systems. Section 2 contains a detailed summary of the data used and the modeling techniques employed. Section 3 contains an assessment of the model uncertainties and a description of the error model provided with the WMM2020. Section 4 contains charts of all the magnetic elements at 2020.0 and their expected annual rates of change between 2020.0 and 2025.0. These predicted changes are based upon the best knowledge of the geomagnetic main field evolution at the time the WMM was released. Sponsored by the U.S. National Geospatial-Intelligence Agency (NGA) and the U.K. Defence Geographic Centre (DGC), the World Magnetic Model (WMM) is produced by the U.S. National Oceanic and Atmospheric Administration’s National Centers for Environmental Information (NOAA/NCEI) and the British Geological Survey (BGS). It is the standard model used by the U.S. Department of Defense (DoD), the U.K. Ministry of Defence, the North Atlantic Treaty Organization (NATO) and the International Hydrographic Organization (IHO), for navigation, attitude and heading referencing systems using the geomagnetic field. It is also used widely in civilian navigation and heading systems

Recent secular variation and an update to the World Magnetic Model

The secular variation (SV) and secular acceleration (SA) of the Earth’s geomagnetic field, generated in the outer core, poses a difficult challenge for field modellers. We must decipher the scope of spatial and temporal changes that are often poorly resolved and masked by variations of other field sources, and parameterise our models to represent the observed signals accordingly. In retrospect, we can accurately model variations with observations from the global network of ground observatories and satellites, but for practical purposes, field models are often used to predict the future state of the field. Models such as the International Geomagnetic Reference Field (IGRF) and World Magnetic Model (WMM) are produced on a quinquennial basis, and predict the core field for the subsequent 5 years. These models are widely used in academia, industry and by governmental and international organisations for purposes such as navigation. With our current incomplete understanding of the physics of the outer core and the generation of SV and SA, it is difficult to predict the time variations of the core field. Such model predictions are based on simplifying assumptions and can differ from the real field variations. In recent years, various SV and SA trends have been observed, captured in as much details as has ever been possible by the extensive observation network. With respect to the most recent (2015) releases of the IGRF and WMM, we present an analysis of field variations, such as reported jerks and accelerating core flows in the northern hemisphere, and their impact on such model predictions. In light of this, we also present an out-of-cycle 2018 update to the WMM2015, ahead of the next scheduled release in 2020, to better account for the field variations observed since 2015

Evaluation of candidate geomagnetic field models for IGRF-12

Background: The 12th revision of the International Geomagnetic Reference Field (IGRF) was issued in December 2014 by the International Association of Geomagnetism and Aeronomy (IAGA) Division V Working Group V-MOD (http://www.ngdc.noaa.gov/IAGA/vmod/igrf.html). This revision comprises new spherical harmonic main field models for epochs 2010.0 (DGRF-2010) and 2015.0 (IGRF-2015) and predictive linear secular variation for the interval 2015.0-2020.0 (SV-2010-2015). Findings: The models were derived from weighted averages of candidate models submitted by ten international teams. Teams were led by the British Geological Survey (UK), DTU Space (Denmark), ISTerre (France), IZMIRAN (Russia), NOAA/NGDC (USA), GFZ Potsdam (Germany), NASA/GSFC (USA), IPGP (France), LPG Nantes (France), and ETH Zurich (Switzerland). Each candidate model was carefully evaluated and compared to all other models and a mean model using well-defined statistical criteria in the spectral domain and maps in the physical space. These analyses were made to pinpoint both troublesome coefficients and the geographical regions where the candidate models most significantly differ. Some models showed clear deviation from other candidate models. However, a majority of the task force members appointed by IAGA thought that the differences were not sufficient to exclude models that were well documented and based on different techniques. Conclusions: The task force thus voted for and applied an iterative robust estimation scheme in space. In this paper, we report on the evaluations of the candidate models and provide details of the algorithm that was used to derive the IGRF-12 produc

Out-of-Cycle Update of the US/UK World Magnetic Model for 2015-2020

In early 2018, the World Magnetic Model 2015-2020 (WMM2015) was predicted to exceed its performance specification error tolerances by the end of 2018 or early 2019. Specifically, the grid variation root-mean-square error was about to exceed the 1 degree specification (MIL-PRF89500A) due to fast fluid flows in the Earth’s outer core, especially in the North polar region. An out-of-cycle update of the WMM2015 was developed and released in early 2019 (WMM2015v2) to address this performance degradation. There was a pre-release in September 2018 and this technical note confirms the information provided in that pre-release. It also provides a description of the new model (section 1), how it was produced (section 2) and its uncertainties (section 3). How to Use this Note: A complete description of the WMM2015 is provided in the WMM2015 Technical Report (Chulliat et al., 2015; WMM2015-TR hereafter (http://nora.nerc.ac.uk/id/eprint/510709/)). This new technical note should be seen as an addendum to the WMM2015-TR. It is organized in the same manner as the WMM2015-TR in order to facilitate the retrieval of information by users. It only includes information that is new for the out-of-cycle update, hereafter referred to as WMM2015v2

The Swarm Initial Field Model for the 2014 geomagnetic field

Data from the first year of ESA's Swarm constellation mission are used to derive the Swarm Initial Field Model (SIFM), a new model of the Earth's magnetic field and its time variation. In addition to the conventional magnetic field observations provided by each of the three Swarm satellites, explicit advantage is taken of the constellation aspect by including east-west magnetic intensity gradient information from the lower satellite pair. Along-track differences in magnetic intensity provide further information concerning the north-south gradient. The SIFM static field shows excellent agreement (up to at least degree 60) with recent field models derived from CHAMP data, providing an initial validation of the quality of the Swarm magnetic measurements. Use of gradient data improves the determination of both the static field and its secular variation, with the mean misfit for east-west intensity differences between the lower satellite pair being only 0.12 nT

A 2015 International Geomagnetic Reference Field (IGRF) candidate model based on <i>Swarm’s</i> experimental absolute magnetometer vector mode data

International audienceEach of the three satellites of the European Space Agency Swarm mission carries an absolute scalar magnetometer (ASM) that provides the nominal 1-Hz scalar data of the mission for both science and calibration purposes. These ASM instruments, however, also deliver autonomous 1-Hz experimental vector data. Here, we report on how ASM-only scalar and vector data from the Alpha and Bravo satellites between November 29, 2013 (a week after launch) and September 25, 2014 (for on-time delivery of the model on October 1, 2014) could be used to build a very valuable candidate model for the 2015.0 International Geomagnetic Reference Field (IGRF). A parent model was first computed, describing the geomagnetic field of internal origin up to degree and order 40 in a spherical harmonic representation and including a constant secular variation up to degree and order 8. This model was next simply forwarded to epoch 2015.0 and truncated at degree and order 13. The resulting ASM-only 2015.0 IGRF candidate model is compared to analogous models derived from the mission's nominal data and to the now-published final 2015.0 IGRF model. Differences among models mainly highlight uncertainties enhanced by the limited geographical distribution of the selected data set (essentially due to a lack of availability of data at high northern latitude satisfying nighttime conditions at the end of the time period considered). These appear to be comparable to differences classically observed among IGRF candidate models. These positive results led the ASM-only 2015.0 IGRF candidate model to contribute to the construction of the final 2015.0 IGRF model

International Geomagnetic Reference Field: the 12th generation

The 12th generation of the International Geomagnetic Reference Field (IGRF) was adopted in December 2014 by the Working Group V-MOD appointed by the International Association of Geomagnetism and Aeronomy (IAGA). It updates the previous IGRF generation with a definitive main field model for epoch 2010.0, a main field model for epoch 2015.0, and a linear annual predictive secular variation model for 2015.0-2020.0. Here, we present the equations defining the IGRF model, provide the spherical harmonic coefficients, and provide maps of the magnetic declination, inclination, and total intensity for epoch 2015.0 and their predicted rates of change for 2015.0-2020.0. We also update the magnetic pole positions and discuss briefly the latest changes and possible future trends of the Earth’s magnetic fiel