On the effective number of climate models

Projections of future climate change are increasingly based on the output of many different models. Typically, the mean over all model simulations is considered as the optimal prediction, with the underlying assumption that different models provide statistically independent information evenly distributed around the true state. However, there is reason to believe that the assumption of model independence is unfounded. Coupled models are of comparable complexity and are constructed in similar ways. Some models share parts of the same code and some models are even developed at the same center. This contributes to the well-known problem of common model biases and, consequently, to a reduced spread amongst different predictions. This study attempts to quantify the extent of this problem by asking how many models there effectively are. Determining the effective number of models is achieved by evaluating 24 state-of-the-art models and their ability to simulate broad aspects of 20th century climate. Using two different methods, we quantify the amount of unique information in the ensemble and find that the effective ensemble size is much smaller than the actual number of models. As more models are included in an ensemble, the amount of new information diminishes in proportion. We further find that this reduction goes beyond the problem of "same-center" models and that systemic similarities exist across all models. Our results suggest that current methodologies for the interpretation of multi-model ensembles may lead to overly confident climate predictions.