Climate Change 2001:
Working Group I: The Scientific Basis
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Sensitivity of results
A variety of sensitivity tests confirm that the detection of anthropogenic signals is insensitive to differences between solar forcing reconstructions, the inclusion of additional forcing through the specification of observed stratospheric ozone concentrations, and to varying details of the analysis (including omitting the signal-to-noise optimisation). Tett et al. (1999, 2000) also found that detection of an anthropogenic signal continues to hold even when the standard deviation of the control simulation is inflated by a factor of two. Uncertainty in the signals is unavoidable when ensembles are small, as is the case in Tett et al. (1999), and biases the estimates of the signal amplitudes towards zero. Consistent results are obtained when this source of uncertainty is taken into account (Allen and Stott, 2000; Stott et al., 2000a). However amplitude estimates become more uncertain, particularly if the underlying signal is small compared with internal climate variability. Accounting for sampling uncertainty in model-simulated signals indicates a greater degree of greenhouse warming and compensating aerosol cooling in the latter part of the century than shown by Tett et al. (1999). Gillett et al. (2000b) find that discounting the temperature changes associated with changes in the Arctic Oscillation (Thompson and Wallace, 1998; Thompson et al., 2000), which are not simulated by the model, does not significantly alter the Tett et al. (1999) results.

Confidence intervals and scaling factors
Confidence intervals for the signal amplitudes that are obtained from the regression of modelled signals onto observations can be re-expressed as ranges of scaling factors that are required to make modelled signal amplitudes consistent with those estimated from observations (see, e.g., Allen and Tett, 1999). The results show that the range of scaling factors includes unity (i.e., model is consistent with observations) for both the greenhouse gas and the sulphate aerosol signal, and that the scaling factors vary only to a reasonable (and consistent) extent between 50-year intervals.

The scaling factors can also be used to estimate the contribution from anthropogenic factors other than well-mixed greenhouse gases. Using the methodology of Allen and Stott (2000) on the simulations described by Tett et al. (2000), the 5 to 95% uncertainty range for scaling the combined response changes in tropospheric ozone and direct and indirect sulphate forcing over the last fifty years is 0.6 to 1.6. The simulated indirect effect of aerosol forcing is by far the biggest contributor to this signal. Ignoring the possible effects of neglected forcings and assuming that the forcing can be scaled in the same way as the response, this translates to a -0.5 to -1.5 Wm-2 change in forcing due to the indirect effect since pre-industrial times. This range lies well within that given in Chapter 6 but the limits obtained are sensitive to the model used. Note that large values of the indirect response are consistently associated with a greater sensitivity to greenhouse gases. This would increase this model's estimate of future warming: a large indirect effect coupled with decreases in sulphate emissions would further enhance future warming (Allen et al., 2000b).

Allen et al. (2000a) have determined scaling factors from other model simulations (Figure 12.12) and found that the modelled response to the combination of greenhouse gas and sulphate aerosol forcing is consistent with that observed. The scaling factors ranging from 0.8 to 1.2 and the corresponding 95% confidence intervals cover the range 0.5 to 1.6. Scaling factors for 50-year JJA trends are also easily derived from the results published in Hegerl et al. (2000). The resulting range of factors is consistent with that of Allen et al. (2000a), but wider because the diagnostic used in Allen et al. (2000b) enhances the signal-to-noise ratio. If it is assumed that the combination of greenhouse warming and sulphate cooling simulated by these AOGCMs is the only significant external contributor to inter-decadal near-surface temperature changes over the latter half of the 20th century, then Allen et al. (2000a) estimate that the anthropogenic warming over the last 50 years is 0.05 to 0.11°C/decade. Making a similar assumption, Hegerl et al. (2000) estimate 0.02 to 0.12°C/decade with a best guess of 0.06 to 0.08°C/decade (model dependent, Figure 12.10). The smallness of the range of uncertainty compared with the observed change indicates that natural internal variability alone is unlikely (bordering on very unlikely) to account for the observed warming.

Figure 12.12: (a) Estimates of the "scaling factors" by which we have to multiply the amplitude of several model-simulated signals to reproduce the corresponding changes in the observed record. The vertical bars indicate the 5 to 95% uncertainty range due to internal variability. A range encompassing unity implies that this combination of forcing amplitude and model-simulated response is consistent with the corresponding observed change, while a range encompassing zero implies that this model-simulated signal is not detectable (Allen and Stott, 2000; Stott et al., 2000a). Signals are defined as the ensemble mean response to external forcing expressed in large-scale (>5000 km) near-surface temperatures over the 1946 to 1996 period relative to the 1896 to 1996 mean. The first entry (G) shows the scaling factor and 5 to 95% confidence interval obtained if we assume the observations consist only of a response to greenhouse gases plus internal variability. The range is significantly less than one (consistent with results from other models), meaning that models forced with greenhouse gases alone significantly overpredict the observed warming signal. The next eight entries show scaling factors for model-simulated responses to greenhouse and sulphate forcing (GS), with two cases including indirect sulphate and tropospheric ozone forcing, one of these also including stratospheric ozone depletion (GSI and GSIO respectively). All but one (CGCM1) of these ranges is consistent with unity. Hence there is little evidence that models are systematically over- or under-predicting the amplitude of the observed response under the assumption that model-simulated GS signals and internal variability are an adequate representation (i.e. that natural forcing has had little net impact on this diagnostic). Observed residual variability is consistent with this assumption in all but one case (ECHAM3, indicated by the asterisk). We are obliged to make this assumption to include models for which only a simulation of the anthropogenic response is available, but uncertainty estimates in these single-signal cases are incomplete since they do not account for uncertainty in the naturally forced response. These ranges indicate, however, the high level of confidence with which we can reject internal variability as simulated by these various models as an explanation of recent near-surface temperature change.
A more complete uncertainty analysis is provided by the next three entries, which show corresponding scaling factors on individual greenhouse (G), sulphate (S), solar-plus-volcanic (N), solar-only (So) and volcanic-only (V) signals for those cases in which the relevant simulations have been performed. In these cases, we estimate multiple factors simultaneously to account for uncertainty in the amplitude of the naturally forced response. The uncertainties increase but the greenhouse signal remains consistently detectable. In one case (ECHAM3) the model appears to be overestimating the greenhouse response (scaling range in the G signal inconsistent with unity), but this result is sensitive to which component of the control is used to define the detection space. It is also not known how it would respond to the inclusion of a volcanic signal. In cases where both solar and volcanic forcing is included (HadCM2 and HadCM3), G and S signals remain detectable and consistent with unity independent of whether natural signals are estimated jointly or separately (allowing for different errors in S and V responses). (b) Estimated contributions to global mean warming over the 20th century, based on the results shown in (a), with 5 to 95% confidence intervals. Although the estimates vary depending on which model's signal and what forcing is assumed, and are less certain if more than one signal is estimated, all show a significant contribution from anthropogenic climate change to 20th century warming (from Allen et al., 2000a).

Given the uncertainties in sulphate aerosol and natural forcings and responses, these single-pattern confidence intervals give an incomplete picture. We cannot assume that the response to sulphate forcing (relative to the greenhouse signal) is as simulated in these greenhouse-plus-sulphate simulations; nor can we assume the net response to natural forcing is negligible even though observations of surface temperature changes over the past 30 to 50 years are generally consistent with both these assumptions. Hence we need also to consider uncertainty ranges based on estimating several signals simultaneously (Figure 12.12, right hand panels). These are generally larger than the single-signal estimates because we are attempting to estimate more information from the same amount of data (Tett et al., 1999; Allen and Stott, 2000; Allen et al., 2000a). Nevertheless, the conclusion of a substantial greenhouse contribution to the recent observed warming trend is unchanged.

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