How large does a large ensemble need to be?

Initial-condition large ensembles with ensemble sizes ranging from 30 to 100 members have become a commonly used tool for quantifying the forced response and internal variability in various components of the climate system. However, there is no consensus on the ideal or even sufficient ensemble size for a large ensemble. Here, we introduce an objective method to estimate the required ensemble size that can be applied to any given application and demonstrate its use on the examples of global mean near-surface air temperature, local temperature and precipitation, and variability in the El Nino-Southern Oscillation (ENSO) region and central United States for the Max Planck Institute Grand Ensemble (MPI-GE). Estimating the required ensemble size is relevant not only for designing or choosing a large ensemble but also for designing targeted sensitivity experiments with a model. Where possible, we base our estimate of the required ensemble size on the pre-industrial control simulation, which is available for every model. We show that more ensemble members are needed to quantify variability than the forced response, with the largest ensemble sizes needed to detect changes in internal variability itself. Finally, we highlight that the required ensemble size depends on both the acceptable error to the user and the studied quantity.