5.1. Changes in Near-Surface Temperature on Century Timescales
 We now examine changes from 1897 to 1997 using information about both temporal and spatial changes in near-surface temperature. We make two further simplifying steps. First, since TROP-ANTHRO and ANTHRO are identical for all but the last 2 decades of the twentieth century (when the difference in surface temperature response is small), we use only ANTHRO in this analysis. Second, we make a simple linear transformation of the amplitudes of GHG and ANTHRO to obtain amplitudes of G (greenhouse gases) and SO (sulphates and ozone) as described in section 4 and Appendix B. Tests for degeneracy (section 4.4) suggest that these patterns are different enough that we can reliably estimate the amplitude of G, SO, and NATURAL (response to solar irradiance and volcanic aerosols) signals simultaneously (Table 1).
 We first check that the reduced space in which we carry out the detection procedure provides an adequate representation of the observed changes. When filtered onto the leading eigenvectors of the covariance matrix (see section 4), the observations contain >96% of the variance (Table 1). The best-estimate linear combination of the signals is consistent with the observations as shown by the weighted sum-of-squares of the residuals (Figure 7a and section 4.1) at all truncations. Thus the representation is adequate.
Figure 7. Ratio of the residual to control variance using a logarithmic scale (solid line with triangles) for (a) the century analysis, (b) five sensitivity studies, and (c) all six 50-year analyses of surface temperature. Also shown are the 10–90% values of the ratio under the null hypothesis that CONTROL and residual variances are the same (solid lines with pluses). Note that CONTROL variance has been inflated (see section 4.1 for details). Bold symbols show values outside these limits.
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 All three signals are detected (Figure 8, left), demonstrating that all have had a statistically significant impact on changes in near-surface temperature over the twentieth century. Furthermore, the amplitudes are all consistent with unity; the model is consistent with observations on decadal timescales and on continental to global spatial scales.
Figure 8. Amplitudes and uncertainty ranges for 100-year analysis and for all 50-year analyses for G (red error bar with asterisk), SO (green error bar with diamond), and NATURAL (blue error bar with triangle). Error bars show the 5–95% uncertainty ranges for detection (inner) and amplitude consistency (outer). Best-estimate signal amplitude is shown as a symbol at the center of the bar. Where the inner bars do not include zero (lower line), the signal is detected. Where the outer bars do not cross 1 (upper line), the amplitude of the simulated signal is inconsistent with the observations.
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 Signal-to-noise ratio is large for the anthropogenic signals but is small for NATURAL (first line of Table 1), suggesting that it is significantly noise contaminated. Noise contamination of the signals biases the best estimate toward zero. Hence our detection of NATURAL is probably robust, though its estimated amplitude ranges, and in particular the upper range, are sensitive to this noise contamination [Allen and Stott, 2002].
 We reconstruct the global mean temperature changes from the best-estimate signal amplitudes and simulated responses (Figure 9). From the 1900s to the 1960s, well-mixed greenhouse gases and other anthropogenic effects (largely the indirect effect of sulphate aerosols) almost balance, giving a total anthropogenic warming of ∼0.1 K. Thereafter, anthropogenic effects warm the planet by ∼0.5 K. From the 1950s onward, natural and anthropogenic nongreenhouse gas forcings each cause a cooling of ∼0.1 K. Together, they offset ∼0.2 K of the estimated 0.6 K warming due to greenhouse gases over the same period.
Figure 9. Reconstruction of global mean temperature variations for 1897–1997. Observations (solid line with squares), best-estimate changes (thick dashed line), and best-estimate contributions from G (dotted line with asterisks), SO (dotted line with diamonds), and NATURAL (dotted line with triangles). Also shown is the best-estimate total anthropogenic contribution (dot-dashed line with crosses). All time series were reconstructed from data in which the 100-year mean had first been removed. Shaded region centered on the observations shows the uncertainty range due to internal variability (two-sigma decadal variability computed from ).
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 While Figure 9 shows the best-estimate combination of signals, it is even more important to consider uncertainty ranges. These are most easily summarized in terms of linear trends (Figure 10) over selected periods (the entire century, 1897–1947, and 1947–1997). The uncertainty ranges in the trends were computed by taking the amplitude ranges from the century analysis and applying them to the simulated trends over the three periods; see section 4 for details. Over the twentieth century, anthropogenic forcings cause a warming trend of 0.5 ± 0.15 K/century. The trend due to greenhouse gases is 0.9 ± 0.24 K/century, while the remaining anthropogenic factors cool at a rate of 0.4 ± 0.26 K/century. The uncertainty in the total anthropogenic warming trend is less than the uncertainties in the individual trends, as they are correlated with one another; see below. Over the century, natural forcings contribute little to the observed trend. Our analysis considers only uncertainty in the amplitude of the simulated response and neglects uncertainty in the time dependence of the forcing and in the spatial patterns of response, as well as neglecting uncertainties in the observations. However, our best estimates are consistent with the observations. Furthermore, in a single ensemble of simulations forced with both natural and anthropogenic forcings, changes in simulated near-surface temperature are consistent with those observed [Stott et al., 2000], suggesting that those uncertainties may not be too great.
Figure 10. Best-estimate linear trend and uncertainty ranges (in K/century). Symbols are as in Figure 8, with the addition of total anthropogenic trend (crosses), total trend (pluses), and observed trends (squares). Symbols show best-estimate trend, while error bars show the 5–95% uncertainty range inflated to allow for four-member ensembles.
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 During the first half of the century, greenhouse gases and natural forcings cause warming trends of ∼0.2–0.3 K/century, while other anthropogenic factors produce negligible cooling trends (Figure 10). Over the last half of the century, greenhouse gases warm the climate at a rate of 1.7 ± 0.43 K/century, with natural forcings (largely volcanic aerosol) and other anthropogenic factors (mainly the indirect effect of sulphate aerosols) both causing an estimated cooling trend of ∼0.3 ± 0.2 K/century. Thus, since 1947, changes in aerosol concentrations (anthropogenic and natural) have offset about a third of the greenhouse gas warming.
 Uncertainties in signal amplitudes are correlated, as the signals are not orthogonal. The joint confidence regions allow us to examine these correlated uncertainties. We find that all three simulated signals are consistent with the observations (the signal amplitudes are simultaneously consistent with unity; that is, the point (1,1,1) is within the three-dimensional uncertainty ellipsoid), as are any combination of two signals (that is, all the solid ellipses in Figure 11 include the point (1,1)). The uncertainty ellipse for the two anthropogenic signals has a strong tilt, showing that the amplitudes of these signals are highly correlated (Figure 11a). Thus estimated large amplitudes of G are consistent with estimated large amplitudes of SO; that is, the observations require a larger greenhouse gas warming to accompany a stronger cooling from sulphates. Over the century, there is little tilt between the natural and either of the anthropogenic signals (Figures 11b and 11c). Thus errors in the amplitude of the natural signal have little impact on the estimated amplitude of the two anthropogenic signals. Consequently, the uncertainties in the linear trends (Figure 10) due to NATURAL are independent from those due to SO and G.
Figure 11. The 90% joint confidence regions for the 1897–1997 (solid line), 1907–1957 (dashed line) and 1947–1997 (dot-dashed line) from G SO NATURAL analysis. Shown are the two-dimensional confidence regions for (a) G SO, (b) G NATURAL, and (c) SO NATURAL. In all plots, shading denotes regions where signal amplitudes are less than zero.
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Figure 12. Best-estimate amplitudes (thin line), 5–95% detection uncertainties (shading) and 5–95% amplitude consistency uncertainties (shading plus thick lines) are shown for (top row) the 1897–1997 analysis and two 50-year analyses, (middle row) 1907–1957 and (bottom row) 1947–1997 for (left column) G, (center column) SO, and (right column) NATURAL as a function of truncation.
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 One “technical” issue in optimal detection is the eigenvector truncation used (see section 4.3). Our results are insensitive to truncation for both detection (the shaded inner regions in Figure 12 (top row) do not include zero) and “amplitude consistency” (the shading plus thick lines in Figure 12 include 1).
 If we omit the effect of stratospheric ozone decline, by replacing ANTHRO with TROP-ANTHRO, we find little change in the residuals and find only small changes in the amplitudes. There is a slight reduction in the cooling attributed to sulphate aerosols and tropospheric ozone from the 1950s, which is compensated for by a small increase in naturally forced cooling (not shown).
5.2. Sensitivity to Processing and Variability Estimates
 In this section we explore the sensitivity of results from the previous analysis to details of the data processing and to increases in the magnitude of the simulated climate variability. We consider the following cases: (1)No-weight, where we did not apply the weighting of to the spherical harmonics (see section 4 for details); (2) Exchange, in which we used to optimize and used CN to compute uncertainties; that is, we used HadCM3 data to optimize and used HadCM2 data to compute uncertainties; (3) Index, where, rather than projecting simulated and observed data onto spherical harmonics, three indices were computed: the global average, the land temperature, and the Northern Hemisphere minus the Southern Hemisphere; and (4) 90-year, where, rather than doing the analysis for the century, we carried out the analysis on two 90-year segments (1897–1987 and 1907–1997).
 In the 90-year 1907–1997 and Index sensitivity studies we find that the simulations and observations are inconsistent (section 4.1) at the largest truncations that we consider (Figure 7b). Therefore we truncate at the largest truncations that are consistent with the observations (Table 1). We carry out both 90-year analyses at the truncation determined by the 1907–1997 case.
 We repeat these analyses and the century case at half the largest truncation to see if our results are insensitive to truncation. Thus, including the “normal” data processing at truncation 20, we examine a total of 11 sensitivity studies, giving 12 cases in all. At these truncations the filtered observations contain at least 80% of the observed variance (Table 1), except in two cases.
 The SNR for the anthropogenic signals is always >2, suggesting little noise contamination (Table 1). By contrast, SNR for NATURAL is close to 1 and in five cases is not significantly different from that expected by chance. There is evidence of signal degeneracy (see section 4.4) in five cases (Table 2), meaning that results in those cases may be sensitive to small changes in the signals. We find that (1) G is detected in all cases (Table 2); (2) SO is detected in all but two cases, both at half the maximum truncation; and (3) NATURAL is detected in all but two cases.
Table 2. Sensitivity Studiesa
|90 years, 1897–1987||36||0.95b||0.71b||1.05b|
|90 years, 1897–1987||19||0.79b||0.50||1.07b|
|90 years, 1907–1997||36||1.03b||0.89b||0.70b|
|90 years, 1907–1997||19||0.86b||0.63b||0.97b|
 Our claims of signal detection all rely on simulated internal climate variability. We compute how much the model variability needs to be increased to prevent the detection of the signals in all the cases considered above. The amplitude of the simulated variability needs to be inflated by 2.2–4.8 to nullify our detection of greenhouse gases (Table 3) (an increase in variance of 5–23). However, detection of the SO and NATURAL signals is much less robust. Here, an increase in variability by ∼40% (i.e., doubling the variance) is enough to stop detection of SO and NATURAL in half the cases considered.
Table 3. Ratio of Signal Amplitudes to Uncertainty Rangea
|90 years, 1897–1987||36||3.07||1.54||1.93|
|90 years, 1897–1987||19||2.47||0.91||1.51|
|90 years, 1907–1997||36||4.22||1.93||1.04|
|90 years, 1907–1997||19||3.28||1.21||1.05|
5.3. Surface Temperature Changes on 50-Year Timescales
 We now examine changes on 50-year timescales to allow comparison with the HadCM2 results of T99 and S01. Six 50-year periods, each of five decadal means, are considered: 1897–1947, 1907–1957, … , 1947–1997. At least 85% of the observed variance (Table 1) is captured in these periods. Unlike the century analysis, NATURAL is generally not significantly noise contaminated (Table 1), though the signal-to-noise ratio is below 1.5 for NATURAL and ANTHRO before 1937. NATURAL may be less noise contaminated than in the century analysis because the truncation is smaller as more noisy components of the signal are discarded. (Compare the SNR of the century analysis NATURAL signal at truncation 20 with that at truncation 40 in Table 1). We use the same signal combination (G, SO, and NATURAL) as used in the century analysis and find evidence of signal degeneracy during 1927–1977 and during 1937–1987 (Table 1). The residuals are consistent with the variance computed from CONTROL at almost all truncations and for all periods (Figure 7c).
 Both of the anthropogenic signals (G and SO) are detected in all six 50-year periods, with amplitudes consistent with unity (Figure 8). Natural effects on climate are only detected during the 1907–1957 period (Figure 8), whereas the amplitudes are consistent with unity only in 1897–1947, 1907–1957, and 1927–1977.
 We wish to compare our results with T99 and S01, include the period when NATURAL is detected, and also examine both periods of warming during the twentieth century. Thus we consider in more detail the 1907–1957 and 1947–1997 periods.
 We first of all consider how robust our results are to changes in truncation. Detection of both the anthropogenic signals during these periods, unlike the natural signal, is largely robust to truncation (Figure 12). All signal amplitudes are consistent with unity, except during 1947–1997 for NATURAL at all truncations and for G for truncations below 13.
 Best-estimate global mean temperature changes and trends (section 4) are proportional to the amplitudes shown in Figure 8. Thus we can compare best-estimate changes and trends from the 50-year and century analyses by comparing their amplitudes. The 50-year analyses produce smaller natural changes than the century analysis, except in the 1907–1957 period. Cooling from sulphates and ozone is about the same in both cases, while greenhouse gas warming is less in the 50-year analyses from 1927 onward (Figure 8). Thus total anthropogenic changes and trends are generally smaller in the 50-year analyses than in the century analysis.
 Only in the 1907–1957 analysis do natural forcings make a substantial contribution to temperature trends (Figure 13). In this period the temperature trend due to anthropogenic forcings is close to zero. In this period, amplitudes (Figure 8), and hence temperature trends (Figure 13), of all three signals are also very similar to the century analysis. Note that the trends and uncertainties shown in Figure 10 are computed from scaling factors using the century analysis (section 5.1), while those shown in Figure 13 are computed using a 50-year analysis.
Figure 13. Best-estimate linear trend and uncertainty ranges (in K/century) for 50-year timescale analysis. Colors and symbols are as in Figure 8, with the addition of total anthropogenic trend (pale blue crosses), total trend (black pluses), and observed trends (black squares).
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 In the 1907–1957 analysis the difference between the best estimate and the observed trend (residual) is the largest of all the periods considered (Figure 13). The residual is still consistent with our estimated internal climate variability and so could be due to internal climate variability alone. It could also, partly or wholly, be due to observational error, error in the forcing time series, some other forcing not considered in our analyses, model error, or noise in the signals. T99 found a large residual in their GS SOL analysis (see T99, Figure 2b) in the 1906–1956 period, suggesting that this result is robust to using the solar time series of Hoyt and Schatten , neglecting the effect of volcanos and the use of a different model. Hegerl et al.  found that observational error was much smaller than internal variability. This suggests that the large residual is probably due to internal climate variability. Delworth and Knutson  found that one simulation from an ensemble of anthropogenically forced simulations was similar to the observations of twentieth century near-surface temperature change. However, like us, they found that the ensemble was inconsistent with the observed changes in the early century.
 Thus the 1907–1957 warming is best explained by a combination of natural forcings (an increase in solar irradiance, a lack of large volcanic forcing, and a recovery from earlier volcanic forcing), near-zero response to total anthropogenic forcing, and a large warming from internal climate variability. If correct, this suggests that a large part of the early century warming is due to a combination of natural forcing and natural internal variability. In other words, it is naturally caused. In our simulations, sulphates offset most of the greenhouse warming prior to the 1960s. If this were not the case, then we would be likely to have smaller residuals and thus estimated a smaller contribution from internal climate variability to the early century warming.
 The model is consistent with the observations in the two 50-year periods that we have chosen to focus on (1907–1957 and 1947–1997). In these periods the uncertainty ellipses for the two anthropogenic amplitudes are strongly tilted, showing that their amplitudes are highly correlated (Figure 11a). Amplitudes of the natural and anthropogenic signals are less correlated (Figures 11b and 11c). In 1947–1997 the tilt is such that a larger amplitude of the G signal requires a larger amplitude of the NATURAL signal, whereas the ellipse is weakly tilted in the opposite direction in the 1907–1957 period. The natural and anthropogenic amplitudes are less correlated in the century analysis than in either of the 50-year analyses. Therefore the former analysis is better at discriminating between natural and anthropogenic forcings than is the latter. All three signals are simultaneously consistent with the observations (the point (1,1,1) is inside the three-dimensional ellipsoid centered on ) in all periods except 1917–1967 (not shown).
 We can compare our results with those of T99 and S01, though our experimental design differs from theirs. For example, we included the effects of ozone, while they did not. Unlike T99 and S01, we detect anthropogenic influences in all 50-year periods considered. Our detection of a combined solar and volcanic effect on climate during 1907–1957 corresponds to their detection of a solar influence during 1906–1956. There are differences in the warming during this period (compare our Figure 14a with Figure 1b of T99), some of which may be due to use of the solar forcing of Lean et al. [1995a] rather than that of Hoyt and Schatten . Our total anthropogenic changes for 1947–1997 are similar to those of T99, but with less sulphate cooling and less greenhouse warming than T99; compare our Figure 14b with Figure 1c of T99.
Figure 14. Best-estimate reconstruction of temperature variations for (a) 1907–1957 and (b)1947–1997. Symbols are as in Figure 9, but are reconstructed from data from which the 50-year mean had first been removed.
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 The linear trend and uncertainty range for each signal are comparable with those computed by T99 (compare Figure 2 of T99 with our Figure 13). As in T99, the total anthropogenic warming trend is only greatly different from zero in the 1947–1997 period. There are greater greenhouse warming and sulphate cooling trends in our analysis than in T99 (compare our Figure 13 with Figure 2a of T99) in all but the 1947–1997 period. Thus, while the total anthropogenic warming estimated here (using HadCM3) is similar to that of T99 and S01 (using HadCM2), the partitioning into warming from greenhouse gases and cooling from other anthropogenic forcings is different.
 Finally, as in the earlier century analyses, we omit the effect of stratospheric ozone decline and repeat our analysis. We find that the residuals are similar, except during 1947–1997 when the fit to observations is too good for truncations greater than 17, suggesting that the model may have too much internal variability. Though the same signals are detected, the amplitude of G is significantly smaller than unity in the 1937–1987 and 1947–1997 analyses, meaning that the simulated response is significantly too large. We also find that anthropogenic aerosols and tropospheric ozone offset less greenhouse warming in 1947–1997 than in our original 50-year analysis. Since the near-surface temperature responses in ANTHRO and TROP-ANTHRO are similar, then some of our results may be sensitive to relatively small amounts of noise in the signals. Alternatively, they may be sensitive to the highly uncertain ozone forcing.
5.4. Free-Atmosphere Changes
 Several earlier detection and attribution studies have focused on the changes in the zonally averaged temperature of the free atmosphere [Santer et al., 1996b, 1996a; Tett et al., 1996; AT99]. Although it turns out that the stratospheric changes are not particularly well represented in this study by the truncated eigenvectors of the appropriate covariance matrix, we have included this analysis to show how the new simulations compare with earlier work. In particular, we wish to see if the conclusions in the earlier study still hold when the response to natural forcings is taken into account. We examine the difference between the 10-year zonal mean from 1986–1995 and the 20-year zonal mean for 1961–1980, as given by AT99.
 Earlier, we showed that the changes in the free atmosphere simulated by TROP-ANTHRO and GHG are similar. We therefore do not use GHG in this analysis, examining combinations of TROP-ANTHRO, ANTHRO, and NATURAL. This assumes that the relative amplitudes of the G and SOT responses are as in TROP-ANTHRO. To separate the impact of stratospheric ozone decline from all other anthropogenic effects, we transform the amplitude of the TROP-ANTHRO and ANTHRO signals to give amplitudes of GSOT (all anthropogenic forcings except stratospheric ozone decline) and OS (stratospheric ozone decline on climate); see section 4.5 and Appendix B for details.
 In the three-signal case the maximum truncation of CN is seven. For truncations beyond this, the ratio of the residual to control variance is 3–5 times too large (Figure 15a). At truncation 7 the filtered observations contain 48% of the observed mass-weighted variance (Table 1) compared to 71% at truncation 36 (the truncation we believe is the largest we could reasonably consider, given the estimated DOF of CN; see Table 1). The SNR for the two anthropogenic signals is reasonably high (Table 1), while the SNR for the natural signal is <1.
 The GSOTOS and NATURAL case has residual variance consistent with CONTROL for all truncations less than or equal to seven (Figure 15a). At these truncations, OS and NATURAL are consistent with unity and zero; that is, they are not detected, but the simulated amplitudes could be correct (Figures 15c and 15d). GSOT is detected but is inconsistent with unity (Figure 15b). Its best-estimate value is 0.65, suggesting that the simulated tropospheric response is ∼50% stronger than the observed response.
Figure 15. Sensitivity to truncation for free atmosphere analysis. (a) Ratio of the residual to the CONTROL variance (solid line with asterisks), using a logarithmic scale. Other details of plot are as Figure 7. Note that CONTROL variance has been inflated (see section 4 for details). Vertical dotted line shows truncation 7, the largest truncation for which the residual and CONTROL variance are consistent. Shown as a function of truncation are the best-estimate amplitudes (thin lines), 5–95% detection uncertainties (shading), and 5–95% amplitude consistency uncertainties (shading plus thick lines) for (b) GSOXT, (c) OS, and (d) NATURAL.
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 Our failure to detect NATURAL does not rule out the possibility of a statistically significant natural influence on climate, because the simulated signal is noise contaminated and so could be substantially in error. Furthermore, there remains the possibility that natural effects may have an influence on shorter timescales, for example, the stratospheric warming associated with volcanoes and possible links between changes in the upper tropospheric circulation and the solar cycle [e.g., Salby and Callaghan, 2000; Hill et al., 2001].
 Above truncation 7 the residual variance is ∼3–5 times larger than that of CONTROL (Figure 15a), and we now consider why this might be. The observations filtered by these leading seven eigenvectors do capture the gross features of the tropospheric warming (Figure 16a). However, at this truncation the filtered observations do not show the observed stratospheric cooling (Figure 2b) as seen more clearly in the difference between the raw and the filtered observations (Figure 16b). The raw observations are cooler in the stratosphere and are ∼0.1 K warmer throughout large regions of the troposphere than are the filtered observations. Therefore our failure at truncations greater than seven is probably due to the simulated stratospheric variability being too small, though gross signal error cannot be ruled out. At truncation 7 the best-estimate warming from GSOT is similar to the filtered observations (Figure 16a) in the troposphere.
Figure 16. (a) Observed changes in zonal mean temperature filtered by projection onto the leading seven eigenvectors of CN. A contour interval of 0.1 K is used between 0 K (bold contour) and 0.6 K, with additional contours at −0.2, −0.5, and −1 K and with dark shading above 0.3 K and light shading below −0.2 K. (b) Raw observations minus data from Figure 16a (i.e., what the filtering removes). A contour interval of 0.1 K is used between −0.2 and 0.6 K, with additional contours at −0.5 and 1 K. The zero contour is bold, with light shading for differences below −0.2 K and with dark shading for differences above 0.1 K.
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