SUMMARYThe vertical ux of mass by atmospheric convection, and convective cloud systems in particular, is a key quantity used in parametrization schemes for numerical weather-prediction models and climate models. The concept of formulating mass uxes in terms of statistical quantities is discussed and a probabilistic description of the upward mass uxes, based on extreme-value theory, is presented. This approach is illustrated by a statistical analysis of two-dimensional, numerical realizations of two regimes of tropical convection, namely squall lines and non-squall clusters. Our statistical model allows these distinct cloud systems, which play a key role in determining the shape of the mass-ux pro le, to be ef ciently integrated. Also taken into account is the distinction between mesoscale and convective components of the mass ux.