Supercomputers can help to create more precise forecasts for urgent crises situations. High-velocity input data and varying configuration parameters yield ensembles of huge datasets able to estimate uncertainties in the simulation. Topology data analytics is able to reduce the data size considerable to become feasible to be streamed to the urgent decision makers. We rely on persistence diagrams. New approaches help to speed up the computation of those diagrams and barycenters of ensembles. Additionally, progressive extraction helps to stream intermediate persistence diagram results to the crisis manager for immediate and updated information for visual decision guidance.