Galactic cosmic rays are high-energy charged particles which comprises of protons (⁓89%), alpha particles (⁓10%), and heavier nuclei (⁓1%) which originate from supernova remnants, active galactic nuclei, and other astrophysical sources beyond the heliosphere [2]. These particles, with energies ranging from approximately 10⁶ to 10²⁰ electron volts (eV), travel through interstellar space and encounter the heliosphere, the vast magnetic bubble carved by the solar wind into the interstellar medium. As they propagate inward toward Earth, they interact with the heliospheric magnetic field, which is itself modulated by the 11-year solar activity cycle [3][4].

The mechanism of solar modulation operates through magnetic deflection and diffusion [5]. During periods of high solar activity (solar maximum), the Sun’s magnetic field is strong and complex, with numerous sunspots, frequent coronal mass ejections, and an enhanced interplanetary magnetic field. This turbulent magnetic environment more effectively scatters and deflects incoming cosmic ray particles, reducing their flux at Earth. Conversely, during solar minimum, the heliospheric magnetic field weakens and becomes more ordered, permitting greater GCR penetration to the inner solar system [3].

Importantly, the modulation is energy-dependent. Lower-energy cosmic rays (below ⁓1 GeV) are more strongly modulated by solar activity than their higher-energy counterparts, meaning that the GCR flux reaching different atmospheric depths varies not only temporally but also with geomagnetic latitude and altitude [6]. This energy dependence underpins the rationale for multi-altitude neutron monitor networks: stations at different elevations sampling different portions of the primary cosmic ray spectrum, providing complementary windows into atmospheric ionization processes.

Methane is the simplest hydrocarbon and the most abundant organic trace gas in Earth’s atmosphere [7]. Its atmospheric concentration has risen dramatically since the “Industrial Revolution”, from pre-industrial levels of approximately 722 parts per billion (ppb) to over 1900 ppb by the mid-2020s, a more than 2.5-fold increase unprecedented in at least 800,000 years of ice core records [8]. This rise is responsible for approximately 20% - 25% of the radiative forcing attributable to all well-mixed green-house gases period [1].

The atmospheric methane budget is governed by a dynamic balance between surface emissions and atmospheric sinks. Sources are predominantly anthropogenic (⁓60% of total emissions), which include: fossil fuel extraction and combustion (⁓30%), enteric fermentation in ruminant livestock (⁓20%), and landfills and waste management (⁓10%) [9]. Natural sources which are principally wetlands (⁓30%), termites, wildfires, and geological seeps—constitute the remainder. The primary atmospheric sink (⁓85% - 90%) is oxidation by the hydroxyl radical (OH) in the troposphere, with smaller contributions from stratospheric loss (⁓5%), soil uptake (⁓5%), and reactions with chlorine atoms in the marine boundary layer [10].

The hydroxyl radical (OH), often termed the “detergent of the atmosphere” is the dominant oxidant controlling the lifetime of methane and many other trace gases. OH is produced primarily through photolysis of ozone (O₃) in the presence of water vapor and recycled through reactions with nitrogen oxides (NO_x) and other species [11][12]. Global mean OH concentrations exhibit considerable spatial and temporal variability, with an estimated atmospheric methane lifetime against OH oxidation of approximately 9.1 ± 0.9 years [13]. Critically, any mechanism that modulates OH concentrations whether through changes in UV radiation, water vapor, ozone or ionization can indirectly influence methane concentrations by altering its primary loss rate.

The hypothesis that galactic cosmic rays may influence atmospheric methane rests on several interconnected physical and chemical pathways, with ionization-driven hydroxyl radical production occupying the central mechanistic role.

1.3.1. Ionization and OH Production

When primary cosmic rays enter Earth’s atmosphere, they collide with atmospheric nuclei, initiating extensive particle cascades (air showers) comprising secondary particles which are muons, electrons, neutrons, and protons [14]. These secondary particlees lose energy through ionization, creating ion pairs along their trajectories. The ionization rate varies with altitude, latitude, and solar cycle phase, peaking in the upper troposphere/lower stratosphere (the Pfotzer maximum) at approximately 12 - 15 km altitude [15].

The generated ions participate in a complex web of ion-molecule reactions. In the troposphere and stratosphere, positive ions rapidly transfer charge to water molecules, producing hydrated hydronium ions, while electrons attach to electronegative species, particularly oxygen, forming superoxide ions. Crucially, ion chemistry can enhance OH production through several channels, including direct ion-neutral reactions, ion-induced ozone depletion affecting OH and charge-enhanced nucleation [16][17]. Studies by [16] using the SOCOL chemistry-climate model demonstrated that a 20% increase in GCR flux enhances OH concentrations by 2% - 5% in the upper troposphere and lower stratosphere, with corresponding decreases in methane concentration of approximately 1% - 2%.

1.3.2. Altitude Dependence of Ionization Effects

The altitude dependence of cosmic ray ionization has critical implications for methane chemistry. The energy spectrum of cosmic rays varies with atmospheric depth: higher-energy particles penetrate to the surface, while lower-energy particles are absorbed at higher altitudes. Consequently, the ionization profile peaks in the upper troposphere (⁓10 - 15 km) and decreases toward the surface [15]. This altitude profile is significant because OH distribution is altitude-dependent; with methane lifetime varying with altitude, while cosmic ray ionization maximizes where methane oxidation is most consequential which is near the tropopause, a region critical for stratosphere-troposphere exchange [6].

1.3.3. Alternative and Complementary Mechanisms

While the OH-mediated pathway represents the most direct chemical link between GCRs and methane, several complementary mechanisms warrant consideration. Cloud-mediated radiative effects as posited by [18] and [19] suggest that cosmic ray ionization enhances aerosol nucleation and cloud condensation nuclei formation, increasing low cloud cover and thereby modifying actinic flux and photo-chemistry. On the other hand stratospheric ozone coupling provides an indirect pathway: GCR-induced ionization enhances polar stratospheric NO_x and HO_x, contributing to ozone depletion and increasing UV-B penetration to the troposphere, thereby enhancing OH photoproduction [20]. In addition, electrical effects on cloud microphysics and biogeochemical feedbacks through wetland emissions have been noted to represent further potential coupling pathways [6][21].

The empirical evidence linking cosmic rays to atmospheric composition has accumulated gradually, with mixed results reflecting the challenges of detecting small signals amidst large variability. Earlier work by [22] reported correlations between GCR intensity and various meteorological parameters, though these studies were often criticized for inadequate statistical rigor. However, [16] combined satellite observations with model simulations to estimate that solar cycle variations in GCR flux modulate global methane by approximately 1.5 - 3 ppb. [23] conducted comprehensive testing of cosmic ray-climate correlations, emphasizing the importance of detrending and significance testing. [6] provided an authoritative review concluding that while microphysical mechanisms are well-established experimentally, the magnitude of atmospheric impacts remains uncertain and likely modest.

1) To quantify the statistical relationship between galactic cosmic ray intensity (measured at three differential altitude-diverse neutron monitor stations) and global atmospheric methane concentration between 2006 and 2025.

2) To compare correlation strengths across stations.

3) To evaluate the robustness of correlations through detrended analysis.

Hypothesis: Based on the theoretical mechanism linking GCR-induced ionization to enhanced OH production and accelerated methane oxidation, we hypothesize an inverse correlation between GCR intensity and methane concentration. This anti-correlation is expected to be most pronounced at stations sampling upper tropospheric ionization (high altitude) and to persist after detrending, indicating genuine physical coupling rather than statistical artefact.

GlobalAtmosphericMethaneData. Monthly global average methane mixing ratios (in parts per billion, ppb) were obtained from the NOAA Global Monitoring Laboratory (https://gml.noaa.gov). The dataset spans from 2006 to 2025, comprising 238 monthly observations. These measurements represent zonally averaged surface-level methane concentrations derived from the NOAA cooperative global air sampling network.

CosmicRayIntensityData. Pressure-corrected hourly cosmic ray count rates (1HCOR_E) were obtained from the Neutron Monitor Database (NMDB; https://www.nmdb.eu) for three stations representing different altitudes and geomagnetic cutoff rigidities. Lomnický Štít, Slovakia (LMKS) serves as the high-altitude station, situated at approximately 2634 m above sea level with a geomagnetic cutoff rigidity of approximately 3.84 GV. Mexico City, Mexico (MXCO) serves as the mid-altitude station at approximately 2274 m elevation with a cutoff rigidity of about 8.28 GV. Oulu, Finland (OULU) serves as the low-altitude station at approximately 15 m above sea level with a cutoff rigidity of about 0.81 GV [24]. However, it is important to note that these datasets were resampled to monthly averages to match the temporal resolution of the methane dataset.

DataPairingProcedure. The differing total record lengths (CH₄: n = 238; LMKS: n = 211; MXCO: n = 265; OULU: n = 267) reflect station-specific data availability. For each station, the monthly neutron monitor series was inner-joined with the NOAA monthly CH₄ series on the common year-month index; only months present in both datasets entered the correlation computation as shown in Figure 1. Missing months within the overlap window were handled by listwise deletion with no interpolation or gap-filling.

Figure 1. Temporal coverage of each dataset, showing overlap periods used for correlation analysis.

PearsonProduct-MomentCorrelationCoefficient(r). The Pearson correlation coefficient measures the linear dependence between two continuous variables. It is defined as the covariance of the two variables divided by the product of their standard deviations. The coefficient ranges from −1 (perfect negative linear relationship) to +1 (perfect positive linear relationship), with 0 indicating no linear association [25].

AdaptedtoCosmicRaysandMethane

Let:

G i = galactic cosmic-ray intensity (neutron monitor count rate)

G ¯ = mean cosmic-ray intensity

M ¯ = mean methane concentration

i = time index (month or year)

When different altitudes are factored in, we have

where;

G i , h = Galactic cosmic-ray intensity at an altitude (h)

h = high, mid and low altitudes

SpearmanRankCorrelationCoefficient(ρ). The Spearman rank correlation is a non-parametric measure of monotonic association. Unlike Pearson’s r, it does not assume linearity or normally distributed data; instead, it assesses whether the rank ordering of one variable is consistently related to the rank ordering of another. This is particularly valuable in cosmic ray-climate studies where relationships may be nonlinear or affected by extreme values. Thus the spearman’s ρ was computed using the scipy.stats.spearmanr function in Python [26].

DetrendedAnalysis. Because both methane and cosmic ray time series contain long-term trends (methane has a strong upward trend due to anthropogenic emissions, while cosmic rays exhibit solar-cycle modulation), the raw correlations may be constrained by these secular trends. To address this, a detrended analysis was performed by removing linear trends from both variables using scipy.signal.detrend prior to computing correlations. This isolates shorter-term covariability from long-term drift, providing a clearer picture of any genuine physical coupling [23].

DeseasonalizedAnalysis. In addition to linear detrending, seasonal cycles were explicitly removed from both CH₄ and neutron monitor series by computing monthly climatologies (the mean value for each calendar month across all years) and subtracting them to produce deseasonalized anomalies, which were then linearly detrended. As a further check, first-differenced series

were also analyzed, as differencing simultaneously removes both trend and seasonality while reducing autocorrelation.

Cross-CorrelationLagAnalysis. Cross-correlations between each neutron monitor series and the CH₄ series were computed at integer lags from −36 to +36 months using the Pearson correlation coefficient. For a lag k, the correlation r(k) was computed between the neutron monitor series shifted by k months and the CH₄ series, with both series truncated to the common overlap after shifting. Negative lags denote GCR leading CH₄. P-values at each lag were computed using the standard t-test transformation with n − 2 degrees of freedom and since 73 lags were tested, a Bonferroni correction was applied, yielding an adjusted significance threshold of α_adj = 0.05/73 = 0.00068.

Monthly environmental time series typically exhibit substantial serial autocorrelation, which inflates nominal p-values by reducing the effective degrees of freedom [27]. Two complementary corrections were applied:

EffectiveSampleSize(Bartlett’sFormula). Following [27], the effective degrees of freedom were computed using the autocorrelation functions of both paired series. Applied to the detrended MXCO-CH₄ pair, this yields n* ⁓ 103 (from nominal n = 238), a reduction of approximately 57%.

BlockBootstrap. As a non-parametric alternative, a moving-block bootstrap (block size = 12 months to preserve annual autocorrelation structure, 5000 resamples) was performed to estimate p-values without distributional assumptions.

All statistical computations were performed using Python 3 with the SciPy library (version 1.17.1) [26], while pandas and matplotlib/seaborn were used for data wrangling and visualization respectively. A significance threshold of α = 0.05 was adopted throughout, with results also evaluated at the α = 0.01 and α = 0.001 levels.

Table 1 presents the descriptive statistics for all four variables under study (2006-2025).

Table 1. Descriptive statistics of study variables.

The Pearson correlation analysis found statistically significant relationships between cosmic ray flux and global atmospheric methane at all three stations, though the direction of those relationships differed as shown in Figure 2. LMKS at high altitude showed a moderate positive correlation (r = +0.345), indicating that higher cosmic ray counts were associated with higher methane concentration, while MXCO at mid altitude (r = −0.389) and OULU at low altitude (r = −0.442) both showed negative correlations which is also an indication that higher cosmic ray counts were associated with lower methane concentration as shown in Table 2. The R² values which ranges from about 12% at LMKS to nearly 20% at OULU—confirmed that cosmic ray variability explains a modest but meaningful portion of methane variance. Although the spearman rank correlations broadly agreed on direction at all the three stations, it however revealed an important warning signal at MXCO and OULU, where the Spearman values were substantially weaker than their Pearson counterparts. Thus, this suggests that the linear relationships at those stations were being inflated by outliers, non-linearity, or the shared long-term trends embedded in the raw data.

Figure 2. Scatter plots with linear regression lines showing CR intensity vs. methane at each altitude station.

Table 2. Complete correlation analysis results.

Note. p < 0.001; p < 0.01; p < 0.05; ns = not significant.

The detrended analysis as shown in Figure 3, which strips out the long-term drifts from both variables before computing correlations, proved to be the most revealing component of the analysis. At LMKS, the correlation collapsed from +0.345 to a statistically insignificant +0.051, exposing the high-altitude positive association as a trend artefact with no real physical foundation. Again, at OULU the correlation weakened considerably, though a modest significant correlation survived, which is an indication that its raw result was partly genuine and partly inflated by trend noise. Most interestingly, MXCO stood apart because its correlation remained essentially unchanged after detrending at −0.391 and its Pearson and Spearman values converged to near-identical figures which is a double sign of credibility pointing toward a genuine, robust as well as sub-decadal anti-correlation between cosmic ray intensity and atmospheric methane concentration.

Figure 3. Detrended scatter plots showing CR-methane relationships after removal of linear trends.

Table 3 demonstrates that MXCO retains a significant anti-correlation across all preprocessing methods, though the magnitude decreases with first differencing as expected (differencing emphasizes month-to-month noise over longer-term covariability). LMKS remains insignificant under all methods, confirming it as a statistical artefact. OULU’s marginal significance under linear detrending disappears with more aggressive preprocessing, suggesting its signal is weaker than the linear detrend alone implies.

Table 3. Sensitivity of correlations to preprocessing method.

After adjusting for autocorrelation using the effective sample size (N* ⁓ 103), the MXCO detrended correlation remains highly significant (p < 0.001). The block bootstrap confirms this result (bootstrap p = 0.003). OULU’s adjusted p-value rises to approximately 0.08, rendering it non-significant at the conventional α = 0.05 threshold as shown in Table 4.

Table 4. Autocorrelation-corrected significance (detrended data).

The study period of 2006 to 2025 as shown in Figure 4 spans parts of three consecutive solar cycles. The chart opens during the declining tail of Solar Cycle 23, with the early years (2006-2008) characterised by falling solar activity and rising GCR flux. Solar Cycle 24 ran from January 2008 through December 2019, reaching its official maximum in April 2014 with a double-peaked structure, producing the most prominent trough in neutron monitor counts across all three stations. After Cycle 24, a deep and prolonged solar minimum between 2017 and 2019 allowed GCR flux to climb back to high levels before Solar Cycle 25 began in December 2019, ramping up strongly to its own maximum around October 2024.

Figure 4. Overlaid dual-axis time series showing methane against cosmic ray intensity at each station.

From the chart above, there is a clear upward trend in CH₄ levels over the two decades. This suggests increasing methane emissions over time, potentially from agriculture (livestock, rice paddies), waste, energy production (oil/gas industry), or biomass burning.

At MXCO, the strongest Pearson correlation occurs at a lag of −21 months (r = −0.500, p < 10⁻¹⁴), meaning changes in mid-altitude cosmic ray intensity precede corresponding changes in methane by approximately 21 months. At OULU, the optimal lag is −17 months (r = −0.481, p < 10⁻¹⁴), indicating a somewhat shorter delay. The difference in optimal lag between stations may reflect the fact that lower-energy cosmic rays modulate different atmospheric layers with different response time-scales as shown in Figure 5.

Figure 5. Cross-correlation functions for all three stations. Negative lags indicate GCR leading methane. MXCO peaks at −21 months, OULU at −17 months, and LMKS at +19 months (explanatory).

The LMKS lag profile is qualitatively different. Its peak occurs at +19 months (r = +0.572, p < 10⁻¹⁷), with the positive lag meaning methane leads LMKS cosmic rays by 19 months rather than the reverse. This is physically implausible as a causal mechanism and instead reflects the auto-correlation structure of both trending time series, further confirming that the LMKS-methane relationship is a statistical artefact.

Several limitations should be acknowledged.

1) Correlation does not imply causation, and the observed associations may be mediated by confounding variables not included in this analysis, such as solar UV flux, geomagnetic activity, or stratospheric ozone variability.

2) The study uses global average methane data, which aggregates regional sources and sinks; a regionally disaggregated analysis might reveal clearer cosmic ray-methane signatures.

3) The lag-correlation analysis is exploratory and should be interpreted with caution given the effects of autocorrelation on cross-correlation estimates.