Global mean temperature since 1880 (Hansen and Wilson, personal communication).


Temperature changes since 1880 for IPCC "business as usual" emissions scenario and ΔT2×CO2 = 4°C for various choices of characteristic ocean delay.


Response of global temperature to Krakatoa-type eruption for various choices of characteristic ocean delay.

warming. It is also worth pointing out that none of the choices of leads to more than 3.5"C of warming by the year 2100—despite the fact that effective CO2 is assumed to have quadrupled, and hence for = 4.8°C the equilibrium warming in 2100 would be 9.6°C. This dramatically illustrates the importance of ocean delay.

The question we deal with is whether we can do better than the above in constraining expectations. We wish to suggest that the answer may well be yes. Figure 6 shows T vs. t for = 4°C and various choices of τ (again using the IPCC BAU scenario). Here we see that for = 4°C to be compatible with the observed warming, τ must be greater than 100 years. The point is that natural variability is unlikely to cancel out more than about 0.5°C of warming over relatively short periods. There are, indeed, model results that suggest both = 4°C and short τ's (Manabe et al., 1991), but as we see here, such suggestions are highly problematic.

We finally turn to volcanos. Wigley and Raper (1995) note that atmospheric response to volcanic dust is largely independent of τ because of the short time scales involved. These claims are true only for the first year or two after eruption. For longer times, there are significant dependencies. We represent the forcing from a volcano as ΔS = kt for t ≤ 3 months, and ΔS = S0e−t/d for t > 3 months, where S0 = k × 3 months = 9.3 W m−2, and d = 13 months. These values are crudely chosen to correspond to Krakatoa (Oliver, 1976). Figure 7 shows the response to a single eruption for various choices of τ (or, equivalently, of gain, using Figure 2). We see that we can expect a cooling of 0.25-0.35°C within a year or two of eruption, regardless of climate gain.3 However, for large τ (or system gain) long-term behavior is very different. For short τ's (τ < 16 years or g < 0.5) the cooling maximizes by t = 1 year and decays to relatively undetectable levels within less than 10 years. However, for longer τ's almost half the maximum cooling persists for many years. Also, the maximum cooling seems to occur at t = 2 years rather than 1 year. Neither of these features has been much remarked on. What is going on is that the short-term volcanic cooling is disequilibrating the surface temperature vis-à-vis both the atmosphere and the ocean. For long τ'S, the atmospheric coupling is weak and the ocean delay plays a larger role. Detecting such differences for a single volcano is likely to be non-trivial. Figure 8, from Hansen et al. (1992), shows predicted responses to Pinatubo in a general-circulation model with different assumed greenhouse-warming scenarios. The upper panel clearly shows that Pinatubo leaves


Hansen et al. (1992) claimed that the prediction of cooling following the eruption of Pinatubo constituted an "acid test" of their model. They failed to indicate what aspect of their model was being tested. The prediction certainly did not constitute a test of the predictions of climate response to increasing greenhouse gases.

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