Cumulus convection constitutes a key process in the control of tropical precipitation and the vertical transport of atmospheric water. To better understand the influence of convective processes on the isotopic composition of precipitation and water vapor, water stable isotopes (H218O and HDO) are introduced into a single column model including the Emanuel convective parameterization. This paper analyzes unidimensional simulations of the tropical atmosphere in a state of radiative‐convective equilibrium, and simulations forced by data from the Tropical Ocean–Global Atmosphere–Coupled Ocean‐Atmosphere Response Experiment (TOGA‐COARE). This study shows that deep convective atmospheres are associated with robust isotopic features such as an isotopic composition of the air below the tropical tropopause layer (around 12–13 km) close to the typical values observed in the lower tropical stratosphere, and an isotopic enrichment of the upper tropospheric water that starts well below the tropopause. It highlights the critical role of condensate lofting and convective detrainment in these features, and the role of convective unsaturated downdrafts in the control of the isotopic composition of precipitation. Finally, it shows that the so‐called “amount effect” primarily reveals the influence of large‐scale atmospheric circulation changes on the isotopic composition of the precipitation, and that temperature changes not associated with circulation changes lead to an “anti–amount effect”. The detailed analysis of the physical processes underlying the “amount effect” is presented in a companion paper.