Confidence intervals for time averages in the presence of long-range correlations, a case study on Earth surface temperature anomalies

Time averages, a standard tool in the analysis of environmental data, suffer severely from long-range correlations. The sample size needed to obtain a desired small confidence interval can be dramatically larger than for uncorrelated data. We present quantitative results for short- and long-range correlated Gaussian stochastic processes. Using these, we calculate confidence intervals for time averages of surface temperature measurements. Temperature time series are well known to be long-range correlated with Hurst exponents larger than 1/2. Multidecadal time averages are routinely used in the study of climate change. Our analysis shows that uncertainties of such averages are as large as for a singleyear of uncorrelated data