## Comparisons of the ability of different methods and ensemble sizes to represent the model climate; each panel contains results from the variable and forcing scenario of the corresponding panel in figure 3

**Figure 4.** Comparisons of the ability of different methods and ensemble sizes to represent the model climate; each panel contains results from the variable and forcing scenario of the corresponding panel in figure 3. Plots show the KS statistic between a 10 000 member IC ensemble distribution constructed at 30 (blue) and 60 (red) years into a simulation with different methods of distribution construction. The right side of each subplot uses distributions constructed at the given time point (referred to as 'instantaneous' distributions), with varying ensemble size. The left side uses distributions constructed over a thirty year period around the given time point ('kairodic' distributions). Uncertainty is quantified by repeating the process 100 times using different ICs distributed around the same location on the attractor (see figure 1 and the supplementary materials available at stacks.iop.org/ERL/8/034021/mmedia). Dots represent the median; errors are the 10th–90th percentiles.

**Abstract**

Can today's global climate model ensembles characterize the 21st century climate in their own 'model-worlds'? This question is at the heart of how we design and interpret climate model experiments for both science and policy support. Using a low-dimensional nonlinear system that exhibits behaviour similar to that of the atmosphere and ocean, we explore the implications of ensemble size and two methods of constructing climatic distributions, for the quantification of a model's climate. Small ensembles are shown to be misleading in non-stationary conditions analogous to externally forced climate change, and sometimes also in stationary conditions which reflect the case of an unforced climate. These results show that ensembles of several hundred members may be required to characterize a model's climate and inform robust statements about the relative roles of different sources of climate prediction uncertainty.