Changes over time in the accuracy of analytical approximations for geomagnetic cutoff rigidity

Abstract

The geomagnetic cutoff rigidity (Rc) is a key measure of the Earth´s magnetic shielding against charged particles. Rc can be estimated using computationally intensive trajectory-tracing methods requiring millions of particle trajectories or simplified analytical models, the latter often assuming a predominantly dipolar magnetic field. This study explores how the accuracy of analytical approximations evolves over time by comparing them to trajectory-based values from 1900 to 2020 using error statistical comparative parameters. The results obtained indicate growing discrepancies over time, with mean absolute errors increasing and spatial correlations declining as the geomagnetic field departs from dipolar symmetry. Analytical models show their greatest deviations in regions like the South Atlantic Anomaly and near the magnetic poles, but for the simplest model, there appear to be a compensation making the error quite stable in time. Despite these limitations, simple analytical models remain computationally efficient and valuable for capturing large-scale Rc trends. In addition, the simplicity of analytical models ensures their relevance for applications where computational resources are limited or where a rapid understanding of Rc behavior is required. However, as the geomagnetic field continues to decay, the discrepancies between analytical and numerical approaches are expected to grow. Even if currently they already exhibit global absolute errors on the order of 20% in the best cases, on geological timescales, when the field eventually returns to a predominantly dipolar state and with a dominance higher than the current of ∼80%, these formulas will regain their usefulness.