Understanding the Distribution of Multimodel Ensembles

When analyzing multimodel climate ensembles it is often assumed that the ensemble is either truth centered or that models and observations are drawn from the same distribution. Here we analyze CMIP5 ensembles focusing on three measures that separate the two interpretations: the error of the ensemble mean relative to the error of individual models, the decay of the ensemble mean error for increasing ensemble size, and the correlations of the model errors. The measures are analyzed using a simple statistical model that includes the two interpretations as different limits and for which analytical results for the three measures can be obtained in high dimensions. We find that the simple statistical model describes the behavior of the three measures in the CMIP5 ensembles remarkably well. Except for the large-scale means we find that the indistinguishable interpretation is a better assumption than the truth centered interpretation. Furthermore, the indistinguishable interpretation becomes an increasingly better assumption when the errors are based on smaller temporal and spatial scales. Building on this, we present a simple conceptual mechanism for the indistinguishable interpretation based on the assumption that the climate models are calibrated on large-scale features such as, e.g., annual means or global averages.