Short-Term Temperature Trends within Long-Term Warming

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The Earth's global average surface temperature from 1970 to 2009 can be modeled as a random walk with a warming trend. Despite the overall warming trend, short time periods can show cooling. Explore how the likelihood of short-term cooling in a random walk with a warming trend depends on the length of the time period and compare with the Earth's surface temperature.

Contributed by: Jeffrey B. Weiss (March 2010)
Open content licensed under CC BY-NC-SA



The global surface temperature of the Earth since 1970 can be approximated by an ARMA(1,1) process plus a linear warming trend [1, 2]. The dataset used for the Earth's surface temperature is the monthly global-mean Land-Ocean Temperature Index from the Goddard Institute for Space Studies at NASA [3]. The parameters for the ARMA(1,1) process were obtained by removing the trend from the temperature record and then fitting to an ARMA(1,1) process using the statistical software package R [4]. The probability of seeing a short-term cooling trend was obtained from simulating the resulting ARMA(1,1) process plus trend for 100,000 years. This Demonstration was inspired by a blog post at Open Mind [5].


[1] J. D. Cryer and K.-S. Chan, Time Series Analysis With Applications in R, New York: Springer, 2008.

[2] H. von Storch and F. W. Zwiers, Statistical Analysis in Climate Research, Cambridge: Cambridge University Press, 1999.

[3] Goddard Institute for Space Studies Surface Temperature Analysis.

[4] The R Project for Statistical Computing.

[5] Open Mind, "Don't Get Fooled, Again".

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