Atmospheric CO<sub>2</sub> concentrations show (i) a global trend, (ii) a seasonal cycle that varies with location and altitude and (iii) inter-annual and synoptic variability. The CO<sub>2</sub> atmospheric inversion of the Copernicus Atmosphere Monitoring Service (CAMS) constrained by surface measurements of the gas concentration provides a 4D (spatial+time) description of the CO<sub>2</sub> mixing ratio. A comparison of the CAMS modelling against AirCore profiles acquired over France indicates an accuracy on the order of 1 ppm (CO<sub>2</sub>) at most levels in the atmosphere with larger errors close to the surface. In this paper, we attempt a simple description of the concentration time series where the trend is provided by the Mauna Loa measurement dataset and the seasonal cycle is adjusted by an annual and semi-annual sinusoidal function. Most of the atmospheric concentration variability is captured by this simple modelling. Over France, the difference between simulated concentrations and in-situ (AirCore) measurements are on the order of 1.5 ppm over the free troposphere and higher. The evaluation against column concentration retrievals from the Total Carbon Column Observing Network (TCCON) indicates typical errors better than 1 ppm for the full atmospheric modelling and on the order of 1 ppm for the climatological fit.</p> <p>The climatological product is updated in near-real time with the Mauna Loa measurements and may be therefore be used for a-priori information for ground-based and satellite based remote sensing of the column-averaged dry air mole fraction of CO<sub>2</sub> (XCO<sub>2</sub>).