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Journal Article

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

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Massah,  Mozhdeh
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Kantz,  Holger
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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http://www.eike-klima-energie.eu/uploads/media/langfrist.pdf
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Citation

Massah, M., & Kantz, H. (2016). Confidence intervals for time averages in the presence of long-range correlations, a case study on Earth surface temperature anomalies. Geophysical Research Letters, 43(17), 9243-9249. doi:10.1002/2016GL069555.


Cite as: https://hdl.handle.net/11858/00-001M-0000-002B-BC49-D
Abstract
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.