Atmospheric Correction Methodology & Physical Framework

Cosmic ray muon fluxes observed at ground level are modulated by local atmospheric conditions. To isolate primary cosmic ray variations and heliospheric phenomena, the raw count rates are corrected for atmospheric pressure and temperature variations using a static atmospheric correction model.

1. Physical Model & Atmospheric Corrections

The corrected rate \(R_{\mathrm{corrected}}(t)\) is derived from the observed raw count rate \(R_{\mathrm{raw}}(t)\) at 2-minute resolution via the linear modulation equation (Duperier, 1949; Dorman, 2004):

\[ R_{\mathrm{corrected}}(t) = \frac{ R_{\mathrm{raw}}(t) }{ 1+ \beta\,[P(t)-P_{\mathrm{roll}}(t)] + \alpha\,[T_{\mathrm{eff}}(t)-T_{\mathrm{roll}}(t)] } \]

Where:

\(R_{\mathrm{raw}}(t)\) is the observed raw muon count rate binned at 2-minute intervals [Hz].
\(P(t)\) is the surface pressure [hPa] obtained from a local sensor next to the detector.
\(T_{\mathrm{eff}}(t)\) is the atmospheric effective temperature [K], calculated across pressure levels from ground to the stratosphere using ERA5 reanalysis (Hersbach et al., 2020), validated using onsite daily radiosondes measurements (Grigioni et al., 2022).
\(P_{\mathrm{roll}}(t)\) and \(T_{\mathrm{roll}}(t)\) are reference baselines computed as 24-hour centered moving averages to represent local climatological conditions.
\(\beta\) is the barometric coefficient [%/hPa].
\(\alpha\) is the effective temperature coefficient [%/K].

2. Effective Temperature (\(T_{\mathrm{eff}}\)) Calculation

The temperature effect on cosmic ray muons arises from the competition between pion decay

\[ \pi \rightarrow \mu + \nu \]

and interaction in the upper atmosphere. Higher stratospheric temperatures reduce atmospheric density, increasing the mean free path of pions and allowing more to decay into muons before interacting (Barrett et al., 1952).

Since muons are produced at various altitudes, \(T_{\mathrm{eff}}\) is evaluated as a weighted average of the vertical atmospheric temperature profile \(T(p)\) (Barrett et al., 1952; Grashorn et al., 2010):

\[ T_{\mathrm{eff}}(t) = \frac{ \displaystyle\int_0^{p_0} T(p,t)W(p)\,dp }{ \displaystyle\int_0^{p_0} W(p)\,dp } \approx \frac{ \displaystyle\sum_i T(p_i,t)W(p_i)\Delta p_i }{ \displaystyle\sum_i W(p_i)\Delta p_i } \]

Where:

\(T(p_i,t)\) is the temperature at pressure level \(p_i\) extracted from ERA5 reanalysis vertical profiles (15 isobaric levels).
\(p_0\) is the local surface pressure.
\(W(p_i)\) is the temperature weight function representing the altitude-dependent probability of muon production and survival down to the surface level (Tilav et al., 2010).

3. Calibration Protocol & Parameter Estimation

Temporal Discretization

Calibration regressions are performed on 1-hour aggregated datasets. The 1-hour binning yields low statistical noise in muon counts while matching the temporal grid of the ERA5 reanalysis.

Sliding Window Regression

To eliminate seasonal distortions and localized instrumentation shifts, multi-variable linear regressions are performed over a sliding 20-day window.

Robust Parameter Selection

The overall values of \(\beta\) and \(\alpha\) are set to the robust median values calculated across the multi-day sliding windows over the operational period.

Academic References

Barrett, P. H., Bollinger, L. M., Cocconi, G., Eisenberg, Y., & Greisen, K. (1952). Interpretation of Cosmic-Ray Measurements Underground. Physical Review, 85(2), 285–302.

Dorman, L. I. (2004). Cosmic Rays in the Earth’s Atmosphere and Underground, vol. 303. Springer, New York.

Duperier, A. (1949). The meson intensity at the surface of the earth and the temperature at the production level. Proceedings of the Physical Society. Section A, 62(11), 684.

Grashorn, E. W., de Jong, J. K., Goodman, M. C., Habig, A., Marshak, M. L., Mufson, S., Osprey, S., & Schreiner, P. (2010). The atmospheric charged kaon/pion ratio using seasonal variation methods. Astroparticle Physics, 33(3), 140–156.

Grigioni, P., Camporeale, G., Ciardini, V., De Silvestri, L., Iaccarino, A., Proposito, M., & Scarchilli, C. (2022). Dati meteorologici della Stazione meteorologica CONCORDIA presso la Base CONCORDIA STATION (DomeC). ENEA. DOI: 10.12910/DATASET2022-002.

Hersbach, H., Bell, B., Berrisford, P., et al. (2020). The ERA5 global reanalysis. Quarterly Journal of the Royal Meteorological Society, 146(730), 1999–2049.

Tilav, S., Desiati, P., Kuwabara, T., et al. (IceCube Collaboration). (2010). Atmospheric Variations as Observed by IceCube. Proceedings of the 31st International Cosmic Ray Conference (ICRC 2009), Łódź, Poland.