Experimental setup (scenario 5): Muon data used in this work has been collected with our muon detection system. This muon monitoring system is currently in use for both scientific and industrial purposes (Martínez-Ruiz del Árbol et al., 2022). The particle detectors are composed of four Multi-Wire Proportional Chambers (MWPC) and each chamber has two layers with 224 detection wires, all of them separated by 4 mm. The two layers form a two-dimensional grid of wires which covers an area of 89.6 x 89.6 cm and detects the positions where muons cross it. When a muon event is identified, our system detects four points located in the horizontal two-dimensional grids, two points before the particle goes through the target and another two points after the particle traverses it. With this data, way-in and way-out trajectories can be reconstructed, and muon deviations calculated. Specifically, in the numerical analysis of this work, we utilised the projection of muon deviations in two planes perpendicular to the detection wires. Simulation setup (scenarios 1 to 4): The snowpack was simulated using a one-dimensional snow model forced by surface meteorological data. We have used the SNOWPACK model (Bartelt & Lehning, 2002) to realistically simulate the behaviour of the snowpack along two seasons, 2015/2016 (1_Modelling) and 2016/2017 (2_Testing). SNOWPACK was forced by the ERA5-Land surface reanalysis (Muñoz-Sabater et al., 2021). The simulations were performed in the Pyrenees, using the ERA5-Land cell whose centroid falls closer to the Monte Perdido massif (42.7°N, -0.1°E), at an elevation of 2041m asl. We coupled the SNOWPACK simulations with a full MSR simulation setup that uses the Cosmic RaY generator (Hagmann et al., 2012) to reproduce the atmosphere muon flux and GEANT4 (Agostinelli et al., 2003) to simulate the muon scattering caused by the snowpack. GEANT4 is a state-of-the-art software designed and maintained at CERN to simulate the interactions of part

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