Monitoring the upper atmospheric temperature and interplanetary magnetic field with the GRAPES-3 muon telescope

Galactic Cosmic Rays (GCRs) have to travel through the heliosphere before they interact with the Earth’s atmosphere. During this, they are deflected by the Sun’s magnetic field, causing variations in this field to imprint on the flux, spectrum and angular distribution of GCRs detected at or near Earth. Studies of these variations over the past several decades have revealed the impact of both transient phenomena such as solar flares, coronal holes, sunspot activity and coronal mass ejections (CMEs) as well as their effects such as Forbush Decreases (FDs), precursors and Ground-Level Enhancements (GLEs). Periodic variations, such as due to the solar diurnal modulation, the 27-day solar rotation, the 11-year solar cycle, and the 22-year solar magnetic cycle have also been characterized. These Sun-induced phenomena are most prominent in GCR intensity variations up to $\sim$30 GeV/nuc, beyond which the influence of solar modulation decreases rapidly as the gyro-radii of GCRs exceed the characteristic size of the heliosphere ($\sim$100 AU).

💡 Research Summary

This paper presents a comprehensive analysis of 22 years (2001–2022) of atmospheric muon data recorded by the GRAPES‑3 muon telescope (G3MT) in Ooty, India, with the aim of quantifying the simultaneous influence of upper‑atmospheric temperature and the interplanetary magnetic field (IMF) on the muon flux. The GRAPES‑3 instrument consists of a 560 m² muon telescope composed of 16 modules, each providing 10‑second resolution measurements in 225 angular bins, yielding roughly 4 × 10⁹ muons per day and statistical uncertainties below 0.01 %.

Data preprocessing involved correcting for atmospheric pressure (β = ‑0.128 % hPa⁻¹) and for long‑term detector efficiency drifts using an automated algorithm based on Bayesian Blocks and Savitzky‑Golay filtering. The muon rates were then averaged over 3‑hour intervals to match the temporal resolution of the atmospheric temperature and IMF datasets.

Upper‑atmospheric temperature was obtained from NASA’s MERRA‑2 reanalysis. Temperatures at 22 pressure levels (775 hPa down to 10 hPa) were interpolated to the GRAPES‑3 site and combined into an effective temperature, T_eff, using an exponential weighting exp(‑x/λ), where x is atmospheric depth and λ is the hadronic attenuation length. The authors adopted λ = 120 g cm⁻² (typical for nucleons) and later examined the robustness of results for λ between 80 and 180 g cm⁻².

IMF data were taken from the ACE and WIND magnetometers at the L1 Lagrange point, accessed via the OMNI database, and similarly averaged to 3‑hour bins. To suppress short‑term fluctuations and isolate the long‑term solar‑cycle modulation, a 60‑day running average was applied to muon, temperature, and IMF time series.

The core methodological innovation is an iterative fitting scheme that simultaneously extracts the temperature coefficient (α_T) and the magnetic‑field coefficient (γ_M) from the muon data. First, a Fast Fourier Transform (FFT) is applied to each time series to isolate the dominant annual modulation and its harmonics. A narrow‑bandpass filter then isolates the spectral components most strongly associated with temperature (annual) and IMF (longer‑term) variations. The muon fractional deviation ΔR/R is modeled as a linear combination: ΔR/R = α_T ΔT_eff + γ_M ΔB. By iteratively adjusting α_T and γ_M to minimize the residuals, the authors achieve convergence to stable values that are statistically independent of each other.

The resulting coefficients are:

• Temperature coefficient α_T = ‑0.2241 % K⁻¹ with statistical uncertainty ±0.0003 % K⁻¹ and systematic uncertainty ±0.0220 % K⁻¹.
• Magnetic‑field coefficient γ_M = ‑0.574 % nT⁻¹ with statistical uncertainty ±0.027 % nT⁻¹ and systematic uncertainty ±0.011 % nT⁻¹.

The negative sign of α_T indicates that an increase in upper‑atmospheric temperature leads to a reduction in the detected low‑energy muon flux. This is consistent with the physics of low‑energy muons (few GeV) produced at altitudes 6–30 km: atmospheric warming expands the air column, lengthening muon paths and raising the probability of decay before reaching the ground. This behavior contrasts with high‑energy muon detectors (e.g., IceCube, MINOS), which exhibit a positive temperature coefficient because warmer air enhances meson decay, increasing the production of high‑energy muons that survive to depth.

The negative γ_M reflects the well‑known modulation of Galactic Cosmic Rays (GCRs) by the heliospheric magnetic field: a stronger IMF deflects more GCRs, reducing the primary flux that generates atmospheric muons, while a weaker IMF permits a higher GCR intensity, raising muon rates.

Robustness checks show that varying λ within the plausible range (80–180 g cm⁻²) changes α_T and γ_M by less than the quoted systematic errors, confirming that the results are not overly sensitive to the assumed attenuation length. Seasonal analysis reveals that during solar minima (e.g., 2008–2009, 2019–2020) the anti‑correlation between muon flux and temperature is strongest, whereas during solar maxima the IMF contribution becomes more prominent, partially masking the temperature effect.

The practical implication is that, with the calibrated coefficients, the GRAPES‑3 muon telescope can serve as a real‑time proxy for upper‑atmospheric temperature (to within ~10 % accuracy) and for the IMF magnitude at L1 (to within ~6 % accuracy) using only the muon count rate. This capability offers a complementary, continuous ground‑based monitoring tool to satellite observations, especially valuable for regions where satellite coverage is limited or where high temporal resolution is required.

The authors conclude by suggesting future extensions: incorporating energy‑dependent attenuation lengths, applying more sophisticated spectral separation techniques, and integrating data from other muon observatories at different latitudes and altitudes to build a global network for simultaneous atmospheric and heliospheric monitoring.