This note summarizes the characteristics of different topological methods for sampling vertical profiles of heterogeneous variables, like atmospheric temperature and water-vapour concentration. The methods presented follow the approach developed for the successive Thermodynamic Initial Guess Retrieval (TIGR) databases at Laboratoire de Météorologie Dynamique. The most recent one is applied to select limited numbers of profiles (some thousands) by the sampling of a much larger dataset (more than one million profiles) from the European Centre for Medium-Range Weather Forecasts short-range forecasts. The sampled datasets are then used for (raining a neural-net work-based radiative-flux profile computation model (NeuroFlux).