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Richard L. Smith
Tom M. L. Wigley
, and
Benjamin D. Santer


A bivariate time series regression approach is used to model observed variations in hemispheric mean temperature over the period 1900–96. The regression equations include deterministic predictor variables and lagged values of the two predictands, and two different forms of this basic structure are employed. The deterministic predictors considered are simple linear trends, various climate model–generated time series based on different combinations of greenhouse gas, sulfate aerosol, and solar forcing, and the Southern Oscillation index (SOI). With linear trends as the only predictors, the best model is a fourth-order bivariate autoregressive model including lagged Southern Hemisphere (SH) to Northern Hemisphere (NH) dependence, as in previous work by Kaufmann and Stern. The estimated NH and SH trends are both +0.67°C century−1, and both are highly statistically significant. If SOI is included as an additional predictor, however, a first-order time series model, with no SH to NH dependence, is an adequate fit to the data. This shows that SOI may be an important covariate in this kind of analysis. Further analysis uses climate model–generated forcing terms representing greenhouses gases, sulfate aerosols, and solar effects, as well as SOI. The statistical analysis makes extensive use of Bayes factors as a device for discriminating among a wide spectrum of possible models. The best fits to the data are obtained when all three forcing terms are included. Total sulfate aerosol forcing of −1.1 W m−2 (with a corresponding climate sensitivity of ΔT = 4.2°C) is preferred to −0.7 W m−2 (with sensitivity of 2.3°C), but the Bayes factor discrimination between these cases is weak.

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