Abstract Increasing the number of heat extremes is the global problem associated with the greenhouse gas (GHG) emissions. The cause-effect relationships between the increase in average temperature and the greenhouse gases contents in the atmosphere are not completely determined. The monitoring data of the gases (methane, water vapor, carbon monoxide and carbon dioxide) and meteorological conditions on the Russia Arctic area, Belyy Island in summer seasons 2015–2017 was used to investigate the cycles of the dynamic change in the variability of the GHG contents. The linear trend of the average values of the temperature or the GHG content in the summer seasons during the three years was not detected. The highest daily mean temperature (283K) in the summer season was corresponding to the hottest 2016. The daily mean GHG concentrations did not differ within the mean plus or minus standard deviation every year. Analysis of the time series of GHG concentrations showed that the methane and water vapor data associated with the temperature contain decade, week, three- and one-day components. The 24- and 72-h time intervals were taken into account to forecast of the seasonal dynamics of the fluctuations by non-linear autoregressive neural network model which provided high predictive accuracy. For a one-day forecast, the correlation coefficients between the predicted and observed GHG contents were near 0.9.

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