We analyzed 12 years (2005–2016) of continuous measurements of atmospheric CO2 and CH4 concentrations made at nine tower observation sites in the Japan–Russia Siberian Tall Tower Inland Observation Network (JR-STATION), located in Siberia. Since the data are very noisy and have a low temporal resolution due to gaps in instrument operation, we used the recently developed Prophet model, which was designed to handle the common features of time series (multiple strong seasonalities, trend changes, outliers) and has a robust performance in the presence of missing data and trend shifts. By decomposing each sampled time-series into its major components (i.e., annual trend and seasonal, weekly, and hourly variation), we observed periodically changing patterns of tracer concentrations. Specifically, we detected multi-year variability of tracers and identified high-concentration events. The frequency of such events was found to vary throughout the year, reaching up to 20% of days for some months, while the number of such events was found to be different for CO2 and CH4. An analysis of weather conditions showed that, in most cases, high-concentration events were caused by a temperature inversion and low wind speed. Additionally, wind directions were found to be different for high- and low-concentration events. For some sites, the wind direction indicated the location of strong local sources of CO2 and CH4. As well as elucidating the seasonality of greenhouse gas concentrations, this study confirmed the potential of the Prophet model for detecting periodicity in environmental phenomena.