Climatic Change

, Volume 118, Issue 3, pp 729-743

First online:

Does temperature contain a stochastic trend: linking statistical results to physical mechanisms

  • Robert K. KaufmannAffiliated withDepartment of Earth and Environment, Center for Energy & Environmental Studies, Boston University Email author 
  • , Heikki KauppiAffiliated withDepartment of Economics, University of Turku
  • , Michael L. MannAffiliated withGeography Department, George Washington University
  • , James H. StockAffiliated withDepartment of Economics, Harvard University

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By construction, the time series for radiative forcing that are used to run the 20c3m experiments, which are implemented by climate models, impart non-stationary movements (either stochastic or deterministic) to the simulated time series for global surface temperature. Here, we determine whether stochastic or deterministic trends are present in the simulated time series for global surface temperature by examining the time series for radiative forcing. Statistical tests indicate that the forcings contain a stochastic trend against the alternative hypothesis that the series are trend stationary with a one-time structural change. This result is consistent with the economic processes that impart a stochastic trend to anthropogenic emissions and the physical processes that integrate emissions in the atmosphere. Furthermore, the stochastic trend in the aggregate measure of radiative forcing also is present in the simulated time series for global surface temperature, which is consistent with the relation between these two variables that is represented by a zero dimensional energy balance model. Finally, we propose that internal weather variability imposed on the stochastic trend in radiative forcings is responsible for statistical results, which gives the impression that global surface temperature is trend stationary with a one-time structural change. We conclude that using the ideas of stochastic trends, cointegration, and error correction can generate reliable conclusions regarding the causes of changes in global surface temperature during the instrumental temperature record.