Abstract. Inaccurate representation of mixing in chemistry transport models, mainly suffering from an excessive numerical diffusion, strongly influences the quantitative estimates of the stratosphere–troposphere exchange (STE). The Lagrangian view of transport offers an alternative to exploit the numerical diffusion for parametrization of the physical mixing. Here, we follow this concept and discuss how to extend the representation of tropospheric transport in the Chemical Lagrangian Model of the Stratosphere (CLaMS). Although the current transport scheme in CLaMS (v1.0) shows a good ability to represent transport of tracers in the stably stratified stratosphere (Pommrich et al., 2014, and the references therein), there are deficiencies in the representation of the effects of convective uplift and mixing due to weak vertical stability in the troposphere. We show how the CLaMS transport scheme was modified by including additional tropospheric mixing and vertical transport due to unresolved convective updrafts by parametrizing these processes in terms of the dry and moist Brunt–Väisälä frequencies. The regions with enhanced convective updrafts in the novel CLaMS simulation covering the 2005–2008 period coincide with regions of enhanced convection as diagnosed from the satellite observations of the outgoing longwave radiation (OLR). We analyze how well this approach improves the CLaMS representation of CO2 in the upper troposphere and lower stratosphere, in particular the propagation of the CO2 seasonal cycle from the planetary boundary layer (PBL) into the lower stratosphere. The CO2 values in the PBL are specified by the CarbonTracker data set (version CT2013B), and the Comprehensive Observation Network for TRace gases by AIrLiner (CONTRAIL) observations are used to validate the model. The proposed extension of tropospheric transport increases the influence of the PBL in the middle and upper troposphere and at the same time impacts the STE. The effect on mean age away from the troposphere in the deep stratosphere is weak.