We present a Lagrangian convective transport scheme developed for global chemistry and transport models, which considers the variable residence time that an air parcel spends in convection. This is particularly important for accurately simulating the tropospheric chemistry of short-lived species, e.g., for determining the time available for heterogeneous chemical processes on the surface of cloud droplets. In current Lagrangian convective transport schemes air parcels are stochastically redistributed within a fixed time step according to estimated probabilities for convective entrainment as well as the altitude of detrainment. We introduce a new scheme that extends this approach by modeling the variable time that an air parcel spends in convection by estimating vertical updraft velocities. Vertical updraft velocities are obtained by combining convective mass fluxes from meteorological analysis data with a parameterization of convective area fraction profiles. We implement two different parameterizations: a parameterization using an observed constant convective area fraction profile and a parameterization that uses randomly drawn profiles to allow for variability. Our scheme is driven by convective mass fluxes and detrainment rates that originate from an external convective parameterization, which can be obtained from meteorological analysis data or from general circulation models. We study the effect of allowing for a variable time that an air parcel spends in convection by performing simulations in which our scheme is implemented into the trajectory module of the ATLAS chemistry and transport model and is driven by the ECMWF ERA-Interim reanalysis data. In particular, we show that the redistribution of air parcels in our scheme conserves the vertical mass distribution and that the scheme is able to reproduce the convective mass fluxes and detrainment rates of ERA-Interim. We further show that the estimated vertical updraft velocities of our scheme are able to reproduce wind profiler measurements performed in Darwin, Australia, for velocities larger than 0.6 ms s-1. SO2 is used as an example to show that there is a significant effect on species mixing ratios when modeling the time spent in convective updrafts compared to a redistribution of air parcels in a fixed time step. Furthermore, we perform long-time global trajectory simulations of radon-222 and compare with aircraft measurements of radon activity.