GMRGE: Geomagnetic Field Components and Solar Wind Parameters in a Coupled Magnetospheric Dynamics Model — Implications for Civil Aviation Safety, 1944–2019

A statistically established association between geomagnetic storms and aircraft accidents has motivated increasingly detailed empirical analyses. Yet, a first-principles physical model linking solar wind (SW) conditions to this association has been lacking. We introduce the Geomagnetic Magneto-Rotational General Energy Equation (GMRGE), a spherical-coordinate magnetohydrodynamic formulation of mass, momentum, and energy conservation linking SW and interplanetary magnetic field (IMF) conditions to Earth-based geomagnetic disturbance (D, H, 𝑧: declination, horizontal, and vertical field components). As a boundary-driven magnetic amplifier, GMRGE maps magnetospheric perturbations directly onto the local Lorentz-force and thermal-conductivity terms that govern aircraft accident risk. Using the IMF clock-angle decomposition of the convection electric field, we derive closed-form expressions for two previously unexplained patterns: the beta paradox, arising from a magnetic-energy-trapping feedback in the model's perpendicular conductivity closure, and the dawndusk asymmetry paradox, arising from the differential sign structure of the model's Lorentz-force terms. Both relations are tested against a 75-year (1944–2019) dataset of 1,758 storm-associated accident records: the beta relation shows a significant, correctly signed correlation with observed plasma beta (Spearman 𝜌 = −0.26, 𝑝 < 10-27), and the asymmetry relation shows a near-perfect rank correlation with its predicted 𝑠𝑖𝑛2(𝜃𝑐) form (Spearman 𝜌 = 0.98, 𝑝 < 10-330). We also report a scale dependence in the composite risk index: significant at the annual/cycle scale (𝑟 = 0.33, 𝑝 = 0.004) but not yet at the individual-storm scale. These results provide the first physics-based, calibrated account of why geomagnetic-aircraft-accident coupling takes the observed functional form.