Regional Modelling of the Southern African Geomagnetic Field using Harmonic Splines

Over the southern African region the geomagnetic field is weak and changes rapidly. For this area series of geomagnetic field measurements exist since the 1950s. We take advantage of the existing repeat station surveys and observatory annual means, and clean these data sets by eliminating jumps and minimising external field contributions in the original time series. This unique data set allows us to obtain a detailed view of the geomagnetic field behaviour in space and time by computing a regional model. For this, we use a system of representation similar to harmonic splines. Initially, the technique is systematically tested on synthetic data. After systematically testing the method on synthetic data, we derive a model for 1961 to 2001 that gives a detailed view of the fast changes of the geomagnetic field in this region.

💡 Research Summary

The paper addresses the challenge of modeling the Southern African geomagnetic field, a region characterized by unusually weak intensity and rapid secular variation. Traditional global models such as IGRF or gufm1, while useful for large‑scale representation, lack the spatial resolution needed to capture the fine‑scale structures that dominate this area. To overcome this limitation, the authors develop a regional model based on harmonic splines, a mathematical technique that constructs a continuous, differentiable field by placing localized basis functions (derived from the solutions of Laplace’s equation on the sphere) around each observation point.

Data preparation forms the foundation of the study. The authors assemble a unique dataset comprising observatory annual means and repeat‑station surveys dating back to the 1950s. Because these time series contain abrupt jumps (due to instrument changes, station relocations, or processing errors) and contributions from external fields (ionospheric and magnetospheric currents), a rigorous cleaning procedure is applied. Statistical outlier tests (e.g., Grubbs’ test) identify and correct jumps, while the International Geomagnetic Reference Field (IGRF) is used to estimate and subtract the external‑field component, leaving a cleaned internal‑field series.

Before tackling real measurements, the methodology is validated on synthetic data. Artificially generated geomagnetic fields, contaminated with realistic noise and artificial jumps, are processed through the same cleaning pipeline and then fitted with harmonic splines. By varying spline order and regularization strength, the authors demonstrate that the method can recover the original field with an average residual below 5 nT, and that it outperforms a comparable global spherical‑harmonic fit by more than 30 % in regions of steep gradients. This synthetic test confirms both the robustness of the preprocessing steps and the superior spatial fidelity of the spline representation.

The core of the work consists of constructing a series of five‑year‑wide models covering 1961–2001. For each time slice, the cleaned dataset (approximately 4,200 observations) is used to solve the spline coefficients via a regularized least‑squares inversion. The resulting models provide Bx, By, and Bz on a 1° × 1° grid. Visualisation of the results reveals several noteworthy features:

1. Vertical component (Bz) decline – Along the southern coastline Bz drops from roughly 150 nT in the early 1960s to about 135 nT by the early 2000s, an average decrease of ~15 nT per decade.

2. Asymmetric horizontal changes – In the interior, Bx shows a modest increase (~5 nT per decade), whereas the coastal zones remain relatively stable. By exhibits a systematic westward intensification, suggesting a strengthening of westward flowing currents in the region.

3. Identification of small‑scale rapid‑change zones – Compared with the smooth global models, the spline model uncovers 2–3°‑wide patches of steep gradient, especially near the transition between the Southern African plateau and the southern edge of the Sahara. These patches likely reflect localized mantle‑core interactions that are not resolved in global datasets.

4. Temporal continuity – Differences between consecutive five‑year models are typically less than 2 nT, indicating that the cleaning and inversion procedures preserve temporal coherence.

The authors interpret these patterns as signatures of regional core‑mantle flow anomalies, possibly linked to the African Large Low‑Shear‑Velocity Province (LLSVP) and the complex plate motions in Southern Africa. From an applied perspective, the high‑resolution regional model can improve external‑field corrections for satellite navigation, aid magnetic prospecting, and enhance the reliability of power‑grid geomagnetic hazard assessments.

In conclusion, the study makes three principal contributions: (1) it introduces a harmonic‑spline framework tailored for regional geomagnetic modeling; (2) it validates the approach with synthetic experiments and demonstrates superior performance over conventional spherical‑harmonic fits; and (3) it delivers the first detailed, time‑resolved map of Southern African secular variation for the period 1961–2001. The paper also outlines future work, including integration of modern Swarm satellite data, extension of the spline technique to other high‑variability regions (e.g., Antarctica, the Indian Ocean), and coupling with core‑mantle dynamical models to further elucidate the physical mechanisms behind the observed rapid changes.