Solar Modulation of Galactic Cosmic Rays and Its Impact on Global Methane Variability

This study investigates the statistical relationship between solar-modulated galactic cosmic ray (GCR) flux and atmospheric methane (CH₄) variability across a multi-altitude network of neutron monitor stations over a 20-year period (2006-2025). Monthly GCR intensity data from three stations spanning a broad altitude range: LMKS at Lomnicky ?tít, Slovakia at 2634 m (high altitude), MXCO at Mexico City, Mexico at 2240 m (mid altitude), and OULU at Oulu, Finland at 15 m (low altitude) were correlated with globally averaged atmospheric methane concentrations from the NOAA Global Monitoring Laboratory using Pearson and Spearman rank correlation coefficients computed via the SciPy statistical library. Raw correlations were statistically significant at all three stations, with LMKS exhibiting a positive association (r = +0.345, p < 0.001) and MXCO and OULU exhibiting negative associations (r = ?0.389 and r = ?0.442 respectively, while p < 0.001 in each case). However, detrended analysis performed to isolate genuine sub-decadal signals from illusions revealed that the LMKS positive correlation is largely spurious (detrended r = +0.051, p = 0.46), driven by coincident long-term drifts rather than a physical mechanism. The MXCO anti-correlation proved most robust, surviving detrending essentially unchanged (r = ?0.391, p < 0.001) with converging Pearson and Spearman coefficients, providing the strongest evidence of a genuine coupling between cosmic ray variability and methane concentration. GCR flux explains up to approximately 20% of methane variance (at OULU). However, after removing long-term trends to isolate sub-decadal covariability, the maximum robust explained variance is approximately 15% (at MXCO), confirming that anthropogenic emissions remain the dominant control on atmospheric methane while solar modulation constitutes a secondary but statistically detectable influence. These findings highlight the altitude-dependent nature of GCR-atmosphere interactions and underscore the necessity of detrended analysis in solar-climate correlation studies.