I currently do research on extreme event characterization, modeling and forecasting using geological data like climate models and observations. For example, are days of extreme temperatures getting more frequent? Or is the annual temperature profile more variable with the current post-industrial climate forcings compared to the pre-industrial era? To answer these questions I look at climate model output, e.g. Global Circulation Models, using different starting conditions and see how their behavior changes statistically.
Related to this is also the desire to incorporate a more statistical framework with the current deterministic climate models. This involves for example adaptive grid sizes and time steps dependent on desired spatio-temporal resolution.