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

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...

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Main Authors: M. Massah, H. Kantz
Format: Article
Language:English
Published: Wiley 2016-09-01
Series:Geophysical Research Letters
Subjects:
Online Access:https://doi.org/10.1002/2016GL069555
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author M. Massah
H. Kantz
author_facet M. Massah
H. Kantz
author_sort M. Massah
collection DOAJ
description 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 single year of uncorrelated data.
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institution Kabale University
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spelling doaj-art-6da2ef41baba47bc9a2f353896f10a4d2025-08-20T03:49:45ZengWileyGeophysical Research Letters0094-82761944-80072016-09-0143179243924910.1002/2016GL069555Confidence intervals for time averages in the presence of long‐range correlations, a case study on Earth surface temperature anomaliesM. Massah0H. Kantz1Max Planck Institute for the Physics of Complex Systems Dresden GermanyMax Planck Institute for the Physics of Complex Systems Dresden GermanyAbstract 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 single year of uncorrelated data.https://doi.org/10.1002/2016GL069555long‐range correlationtime averagesconfidence intervalsEarth surface temperature series
spellingShingle M. Massah
H. Kantz
Confidence intervals for time averages in the presence of long‐range correlations, a case study on Earth surface temperature anomalies
Geophysical Research Letters
long‐range correlation
time averages
confidence intervals
Earth surface temperature series
title Confidence intervals for time averages in the presence of long‐range correlations, a case study on Earth surface temperature anomalies
title_full Confidence intervals for time averages in the presence of long‐range correlations, a case study on Earth surface temperature anomalies
title_fullStr Confidence intervals for time averages in the presence of long‐range correlations, a case study on Earth surface temperature anomalies
title_full_unstemmed Confidence intervals for time averages in the presence of long‐range correlations, a case study on Earth surface temperature anomalies
title_short Confidence intervals for time averages in the presence of long‐range correlations, a case study on Earth surface temperature anomalies
title_sort confidence intervals for time averages in the presence of long range correlations a case study on earth surface temperature anomalies
topic long‐range correlation
time averages
confidence intervals
Earth surface temperature series
url https://doi.org/10.1002/2016GL069555
work_keys_str_mv AT mmassah confidenceintervalsfortimeaveragesinthepresenceoflongrangecorrelationsacasestudyonearthsurfacetemperatureanomalies
AT hkantz confidenceintervalsfortimeaveragesinthepresenceoflongrangecorrelationsacasestudyonearthsurfacetemperatureanomalies