We report measurements of annual and diurnal modulations of the cosmic-ray muon rate in the Yangyang underground laboratory (Y2L) using 952 days of COSINE-100 data acquired between September 2016 and July 2019. A correlation of the muon rate with the atmospheric temperature is observed and its amplitude on the muon rate is determined. The effective atmospheric temperature and muon rate variations are positively correlated with a measured effective temperature coefficient of $alpha_{T}$ = 0.80 $pm$ 0.11. This result is consistent with a model of meson production in the atmosphere. We also searched for a diurnal modulation in the underground muon rate by comparing one-hour intervals. No significant diurnal modulation of the muon rate was observed.
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