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

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Abstract

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.

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Notes

  1. The 20c3m experiments specify the direct effects of sulfur emissions only.

  2. CO2 emissions are the sum of emissions (1850–2000) from land-use change (Houghton, 2008) and emissions from fossil fuels and cement production (Marland et al. 2008).

  3. For example, for CFC12 we have 0.37 = θ87, or θ = 0.371/87 ≈ 0.989.

  4. A stochastic process is called integrated of order d, I(d), d = 0,1,2, …, if Δd X t is I(0), where I(0) is a stationary process and Δ is the difference operator, ΔX t  = X t - X t-1.

  5. This balance is even more complex for radiative forcing of many gases, which are nonlinearly related to concentrations (Eqs. 6–8).

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Authors and Affiliations

  1. Department of Earth and Environment, Center for Energy & Environmental Studies, Boston University, 675 Commonwealth Ave (Room 457), Boston, MA, 02215, USA

    Robert K. Kaufmann

  2. Department of Economics, University of Turku, Rehtorinpellonkatu 3, Turku, 20014, Finland

    Heikki Kauppi

  3. Geography Department, George Washington University, 1922 F St NW, Washington, DC, 20052, USA

    Michael L. Mann

  4. Department of Economics, Harvard University, 1805 Cambridge Street, Cambridge, MA, 02138, USA

    James H. Stock

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  1. Robert K. Kaufmann
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  2. Heikki Kauppi
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  3. Michael L. Mann
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  4. James H. Stock
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Correspondence to Robert K. Kaufmann.

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Kaufmann, R.K., Kauppi, H., Mann, M.L. et al. Does temperature contain a stochastic trend: linking statistical results to physical mechanisms. Climatic Change 118, 729–743 (2013). https://doi.org/10.1007/s10584-012-0683-2

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