Therefore, approaches that fit the tail of the autocorrelation function to an exponential will likely provide superior uncertainty estimates. To illustrate the underestimation of uncertainty, we calculated the percentage of synthetic time series where the estimated 95 % confidence intervals covered the true mean (the coverage) after truncation (Table ). We did this for the "standard" free vanish stage synthetic ensembles, which did not contain initial transients. For the relatively uncorrelated T4L system, the coverage of the confidence intervals were very similar for all methods and close to the expected 95 %. In contrast, for the more correlated PDE2a system, the coverages for all systems were well below 95 %, even though there were still almost 1000 effectively uncorrelated samples. They were worst for the uncorrelated estimate (44 %), and improved up to the N n 0 window method (71 %) as autocorrelation was increasingly accounted for.