Previous research on the temporal evolution of CO2 concentrations focused either on short, local time-scales, or on larger regional time-scales. On these different time-scales the importance of dynamical processes for the CO2 concentration can dier as well. To study this shift of signicance, a model is needed that is able to capture all relevant processes for both short and long time-scales. The purpose of this paper is to extend a mixed-layer model in order to make it suitable for longer time-scales. A mixed-layer model is only valid for convective day-time conditions and can only simulate the convective boundary layer during several hours. By including the theory of Nappo & van Dop (1994) the model will also be suitable for simulating night-time conditions of the mixing ratio of CO2, and as a consequence also longer simulations can be done with it. The results of this extended model are compared with observations of 24-26 September 2003 to assess the accuracy. This shows that the mixing ratio of CO2 is well captured during the rst day and night, but after the transition of night to day the mixing ratio is too low. This is due to incorrect morning conditions (especially the boundary-layer depth), which emphasizes that when modelling the concentration of a chemical compound accurately, first the dynamical characteristics should be correct.