Following on their previous work, in which they found the annular modes to be a preferred response of a simplified general circulation model atmosphere to a number of mechanical forcings, the authors now explore the quantitative relationship between forcing and response. In particular, the applicability of the fluctuation-dissipation theorem to this problem is investigated. First, the set of model trials is expanded by including runs in which the applied forcings are thermal rather than mechanical. For thermal forcings confined to the extratropics, "annular mode-like" responses, reminiscent of those found in earlier work, are found, but, as found in previous studies, the response is less like an annular mode when the forcing has significant amplitude in the tropics. Assuming small departures from the control climatology, and making a few further assumptions, the authors derive a theoretical relationship between forcing and response. This relationship is a statement of the fluctuation-dissipation theorem for this problem. The response of the model is found to be qualitatively consistent with the theoretical predictions. However, several aspects of the response diverge quantitatively from the theoretical expectation.

Measurements show that the Earth's global-average near-surface temperature has increased by about 0.8˚C since the 19th century. It is critically important to determine whether this global warming is due to natural causes, as contended by climate contrarians, or by human activities, as argued by the Intergovernmental Panel on Climate Change. This study updates our earlier calculations which showed that the observed global warming was predominantly human-caused. Two independent methods are used to analyze the temperature measurements: Singular Spectrum Analysis and Climate Model Simulation. The concurrence of the results of the two methods, each using 13 additional years of temperature measurements from 1998 through 2010, shows that it is humanity, not nature, that has increased the Earth's global temperature since the 19th century. Humanity is also responsible for the most recent period of warming from 1976 to 2010. Internal climate variability is primarily responsible for the early 20th century warming from 1904 to 1944 and the subsequent cooling from 1944 to 1976. It is also found that the equilibrium climate sensitivity is on the low side of the range given in the IPCC Fourth Assessment Report.

Previous studies using simplified general circulation models have shown that "annular modes" arise as the dominant mode of variability. A simple GCM is used here to explore to what extent these modes are also the preferred response of the system to generic forcing.A number of trials are conducted under which the model is subjected to an artificial, zonally symmetric angular momentum forcing, and the climatologies of these trials are compared to that of the control. The forcing location is varied among the several trials. It is found that the changes in the model's climatology are generally annular mode-like, as long as the imposed forcing projects strongly upon the annular modes of the unforced model.The role of changes to the eddy-zonal flow feedback versus the action of direct forcing is also considered through the use of a zonally symmetric version of the model. It is found that the direct responses to forcing are insufficient to capture either the strength or the structure of the annular mode responses. Instead, the changes in eddy fluxes are needed to produce the correct responses.

In our original study we crafted trajectories for developed and developing countries that phased-out greenhouse gas emissions during 2015-2065 such that the maximum global warming does not exceed the 2˚C threshold adopted by the UN Framework Convention on Climate Change, and the cumulative emissions for developed and developing countries are identical. Here we examine the effects of increasing the start year from 2015 to 2030 in 5-year intervals, and the phase-out period from 50 to 100 years in 10-year intervals. We find that phase-out during 2020-2100 is optimal. This phase-out increases the year of peak emission from 2015 to 2030 for developed countries and from 2042 to 2053 for developing countries. It also increases the time from peak emissions to zero emissions from 50 to 70 years for developed countries and from 23 to 47 years for developing countries. Both outcomes should facilitate agreement of the Revised Fair Plan by the UNFCCC.

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