Cosmic radiation is a potential additional tool for atmospheric monitoring. High-energy cosmic rays, interacting in the atmosphere, produce secondary particles, the production and propagation of which are ruled by the state of the atmosphere. Atmospheric muons carry information on the stratosphere, as its temperature modulates their intensity. Here, we present a comprehensive investigation of the 24-year series of the muon flux recorded underground with the Large Volume Detector in the Gran Sasso Laboratory in Italy. Using advanced spectral-analysis methods, we reveal, in addition to the well-known annual cycle, two significant variations with periods of about four and ten years. These two multiannual components, however, are not present in the series of the so-called effective temperature—an average parameter commonly used to describe the entire atmospheric profile in relationship to the detected muon flux—but we find them in the series of the raw temperatures in the lower-stratospheric levels. We show that the weaker multiannual cycles emerge in the temperature series thanks to the dampening of the dominant annual radiative cycle at these levels, which are affected by higher-frequency variability related to transport and wave processes. We also show that the multiannual variations are not typical only of the Gran Sasso area but are present at large scales throughout the Northern Hemisphere. The analysis of the series of the muon flux also reveals evidence of daily to monthly scale variations, especially during the highly variable winter period. Although such short-term modulations are also found in the series of the effective temperature, we show that the variations of the two series are brought to better agreement when considering only specific layers of the atmosphere depending on the event. The amplitudes of the multiannual variations are significantly larger than those expected based on the temperature modulations. Such differences may be due to acknowledged difficulties of the adopted temperature reanalysis dataset to thoroughly represent long-term variability scales, so that long-term modulations in the raw temperature series and, consequently, in the effective temperature record would result as artificially attenuated. The muon flux therefore may be envisaged as a high time-resolution integrated proxy of lower-stratospheric temperatures.4 MoreReceived 28 September 2021Accepted 1 February 2022DOI:https://doi.org/10.1103/PhysRevResearch.4.023226Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasAtmospheric scienceTechniquesCosmic rays & astroparticlesGravitation, Cosmology & AstrophysicsInterdisciplinary Physics