Abstract
 Top of page
 Abstract
 1. Introduction
 2. Data
 3. Part 1: Multiple Linear Regressions
 4. Part 2: Scafetta and West Methodologies
 5. Discussion
 6. Conclusions
 Acknowledgments
 References
 Supporting Information
[1] We use a suite of global climate model simulations for the 20th century to assess the contribution of solar forcing to the past trends in the global mean temperature. In particular, we examine how robust different published methodologies are at detecting and attributing solarrelated climate change in the presence of intrinsic climate variability and multiple forcings. We demonstrate that naive application of linear analytical methods such as regression gives nonrobust results. We also demonstrate that the methodologies used by Scafetta and West (2005, 2006a, 2006b, 2007, 2008) are not robust to these same factors and that their error bars are significantly larger than reported. Our analysis shows that the most likely contribution from solar forcing a global warming is 7 ± 1% for the 20th century and is negligible for warming since 1980.
1. Introduction
 Top of page
 Abstract
 1. Introduction
 2. Data
 3. Part 1: Multiple Linear Regressions
 4. Part 2: Scafetta and West Methodologies
 5. Discussion
 6. Conclusions
 Acknowledgments
 References
 Supporting Information
[2] The Intergovernmental Panel on Climate Change (IPCC) report of 2007 assessed that the change in solar radiative forcing (henceforth referred to as “solar forcing”) over the interval 1750–2005 was likely to be in the range 0.12–0.30Wm^{−2}, compared to the total net anthropogenic forcing 1.7Wm^{−2} (0.6–2.4Wm^{−2} [Solomon et al., 2007]). However, detection and attribution of climate change related to longterm solar variability remains a contentious subject, with vastly different estimates appearing in the literature for the 20th century and for more recent decades [e.g., Lean and Rind, 2008; Bard and Delaygue, 2007; Lockwood and Fröhlich, 2007; Lean, 2006; Scafetta and West, 2005, 2006a, 2006b, 2007, 2008; Douglass and Clader, 2002; Benestad, 2002; Stott et al., 2001].
[3] In particular, Scafetta and West [2006a, henceforth “SW06a”] claim that between 25 and 35% of the increase in the global mean temperature 〈T〉 since 1980 can be attributed changes in the solar activity. Note that the 25% and 35% attribution in SW06a was not the range including uncertainties, but their “best” estimates using either ACRIM or PMOD composites of total solar irradiance observations. The actual range including uncertainties would have been much wider. These estimates strongly contrast with independent work indicating that there is no significant trend in the solar activity since 1952, implying that there is no basis for any solarinduced trend since that time [Benestad, 2005; Richardson et al., 2002; Lean, 2006; Lockwood and Fröhlich, 2007].
[4] More recently, Scafetta and West [2007, 2008] presented new calculations from which they concluded that solar forcing may have contributed with as much as 50% or 69% of the observed global temperature increase since 1900. Their research uses a socalled “phenomenological” method based on a fitting procedure to spectral data. Such a large role for solar activity in the warming since 1900 would imply that attribution studies for that period might need to be revisited, but doesn't necessarily imply that the effects of greenhouse gas changes in the future would be affected since uncertainties in the total forcings (including aerosol effects) preclude using the 20th century as a strong constraint on overall climate sensitivity [Annan and Hargreaves, 2006].
[5] Here we try to shed more light on the role of solar forcing by investigating the solar signal in a set of global climate model (GCM) simulations, and then comparing these with corresponding analysis based on the observed temperature record. A suite of 20th century simulations has been performed with GISS ModelE GCM, driven with a full range of estimated forcings over this period as well as with each individual forcing separately [Schmidt et al., 2006; Hansen et al., 2007]. This is a perfect test bed for the various methods, since the “true” amount of solar contribution in each experiment is already known and the amount of interannual “weather noise” and confounding effects (internal variability and response to other forcings) are close to observed.
[6] The error bars on the attribution of the solar component between 1750 and 2005 inferred from IPCC are around 7 to 18% of the total forcing, though since that also includes a negative aerosol component, it might be clearer to say 4 to 11% of the forcings contributing to the warming (including wellmixed greenhouse gases, ozone and black carbon). A full detection and attribution analysis can take into account possible underestimates of the solar forcing and potentially a difference in sensitivity for different forcings (the “efficacy” [IDAG, 2005]). The inferred error bars in the IPCC report do not span the results claims by Scafetta and West, and so there may be systematic issues with the different approaches that have not been sufficiently addressed. In order to help resolve this question, we repeat the analyses of Scafetta and West (hereafter SW) and compare them with a suite of independent analyses, both over the observational data and modelgenerated analogs to test their robustness. The paper is divided into 2 parts, of which the first explores the danger of applying linear statistical methods to data from a complicated and chaotic system. The second part repeats the analyses of SW to explore whether similar problems can affect their results.
5. Discussion
 Top of page
 Abstract
 1. Introduction
 2. Data
 3. Part 1: Multiple Linear Regressions
 4. Part 2: Scafetta and West Methodologies
 5. Discussion
 6. Conclusions
 Acknowledgments
 References
 Supporting Information
[65] The evaluation of the GISS ModelE 〈T〉 simulations, the LCF with solar forcing, and regression studies, suggest that the model approximately reproduces the observed statistical relationships between the global mean temperature and the solar and GHG forcings.
[66] The regression results reported above are only robust for strong forcings, and the values for α and β were consistent for “all” at 1year lag (Tables 3 and 4), but the value for the solar forcing coefficient (β_{1}) was set to zero for the observations as the stepwise screening excluded solar forcings as input for the multiple regression.
[67] One explanation for the “all” experiment yielding a stronger solarinduced trend in 〈T〉 than seen in the observations may be that the GCM was too sensitive to solar forcing. However, another explanation may be that errors in the forcing estimate was exactly correct for the model (by construction), but may not be for the real world. Furthermore, the intrinsic variability also influences the estimates.
[68] We know a priori that the solar forcing coefficient (α_{1}) should be zero for the “GHG” ensemble, but the univariate regression produced _{1} = 0.31 ± 0.03 K/[Wm^{−2}]. Negative values for α_{1} were obtained for “residual” in the univariate analysis, however, the multiple regression against S and ln∣ρ∣ returned positive values. The value for the greenhouse gas coefficient (α_{2}) obtained from the “GHG” ensemble was substantially greater than for “all” and “obs” (Table 3), most likely due to the colinear negative aerosol forcing.
[69] Both F_{S} and F_{GHG} contain trends, and the different forcing components are not mutually orthogonal. Different ensemble members representing the same forced response but different realizations of intrinsic variability give different values for the solar and GHG regression coefficients. The linear regression analysis in part 1 was, however, unable to provide an exact description of the nonlinear response of the complicated climate system, due to the presence of colinearity in the forcings, internal chaotic variations, slow nonlinear response that may produce a more complete response after some time, or “leakage” between the different components [Leroy, 1998].
[70] Additionally, there may also be larger uncertainties in the forcing before 1958, which could affect the results for the observations (though not for the numerical experiments). Benestad [2005] suggested that the sunspot record may have lower quality before 1900, as there was a dramatic change in the solar cycle length characteristics at around the start of the 20th century. Over the interval 1958–2000, the time series for S (little trend) and ln∣ρ∣ were less colinear than over the 1880–2002 period. This may imply that the estimates based on equation (1) and the forcings over 1958–2000 may provide more reliable estimates of the sensitivity.
[71] The coefficient for greenhouse gases from the allforcings multiple regression is _{2} = 0.91 ± 0.19 K/(Wm^{−2}), suggesting a climate sensitivity that is substantially greater than the equilibrium value reported for this model (0.67 K/(Wm^{−2})). Regression coefficients of ∼0.45 K/(Wm^{−2}), on the other hand, imply a transient climate sensitivity that is more consistent with the 1.5–1.6°C reported by Solomon et al. [2007].
[72] The values for solar and greenhouse gas forcing coefficients (α_{1} and α_{2}) may in principle differ if they involve different feedback processes or if other mechanisms are involved. One example could be galactic cosmic rays (GCR) affecting low cloud cover [Carslaw et al., 2002; Dickinson, 1975; Ney, 1959] or solar UV modifying the planetary wave propagation and heat distribution [Shindell et al., 2001]. In these cases the forcing values might be underestimated, hence leading to an apparently larger sensitivity. However, the regression coefficients were similar for both GCM and observations, and the fact that these additional mechanisms were not present in these GISS ModelE simulations, suggest that processes such as GCR are not important, in agreement with Sloan and Wolfendale [2008] and Kristjánsson et al. [2008].
[73] It should be noted that the p values in Table 3 were estimated assuming independent and identically distributed (iid) data, but the presence of autocorrelation lowers the true degrees of freedom. Thus the true p values should be higher than those shown in the tables, and the true error bars should be wider. Furthermore, the regression analysis employed here does not yield robust results when additional forcing terms are included. Similarly, the fact that the regression did not pass the DurbinWatson test for uncorrelated residuals, suggests that the regression was suboptimal. However, the purpose of using regression analysis here was simply to provide a means for comparing different data sets and studying their robustness.
[74] These results reveal the dangers in attributing characteristics of 〈T〉 to similar features in the forcings, and highlight the difficulties associated with detection and attribution more generally. We have also shown through the regression exercises that neglecting important forcings may inflate the climate sensitivity estimates since colinearity between different forcings interferes with the estimation of the sensitivity to each other. This is the main reason why the results produced by the methods in SW06a and SW06b are likely misleading. The key lessons are that detection and attribution has to include all factors (not just a single one) and ensure that results are robust to different realizations of the intrinsic variability.
[75] There is an additional issue with the methodology of SW06a and that is the value they assume for the coefficient Z_{eq} This was taken as the ratio 288 K/(1365 Wm^{−2}) = 0.21 K/[Wm^{−2}]. The choice of this value determines the longterm sensitivity of the climate and is in fact the chief unknown; it can't simply be assumed. Taking this value as the absolute temperature divided by the total irradiance implies that climate change is linear from absolute zero to the presentday temperature, an assumption that is nowhere supported, and to our mind, extremely unlikely. Furthermore, the estimate Z_{eq} = 0.21 K/[Wm^{−2}] implies a climate sensitivity to the TOA radiative forcing of 4.5°C, and the climate sensitivities implied from SW06b were even higher. The adoption of such a high value as used by SW06a and SW06b, has a huge effect on their results.
[76] Variations in Z_{eq} can affect the longterm mean temperature, but not the trends directly. However, the value was used as an upper limit for the values for Z_{S4}, which had a direct bearing on the estimated trends. Spectral analyses and Monte Carlo experiments indicate that the strategy used in SW06a for estimating Z_{11y} and Z_{22y} is prone to noise contamination, thus producing possibly spurious and biased results. The values for Z_{22y} and Z_{11y} had been taken as the ratios between bandpass filtered values of global mean temperature and estimates for S representative for 22year and 11year timescales respectively, despite there being no direct correspondence between the two types of filtered curves [SW05, Figure 4]. In our emulation, we were not able to get exactly the same ratio of amplitudes, due to lack of robustness of the SW06a method and insufficient methods description. If our estimates for Z_{11y} and Z_{22y} were used as parameters in equation (4), we would get unrealistic values for 〈_{sun}〉 (t). Furthermore, the method fails to take the phase information into account, and a weak amplitude in the 22year solar cycle was likely responsible for the spuriously high value for Z_{22y}. The lack of prominent spectral peaks in the power spectrum of observations and the presence of a spectral peak in the reconstructions also suggest that the values for the transfer coefficients were spuriously inflated.
[77] We showed above through Monte Carlo simulations that the ratio between the magnitudes of two similarly bandpass filtered random signals has a distribution with a considerable spread. The conclusions of SW06a therefore hinge on the assumption that none of the variance in the two frequency bands of the temperature was caused by other factors other than solar. This assumption is unlikely to hold.
[78] In an analogous way, the analysis of SW06b was based on the assumption that preindustrial variations in 〈T〉 could entirely be associated with changes in S. This will give an unrealistically high climate sensitivity, since other forcings, particularly volcanic, may also have played a significant role [Shindell et al., 2004]. Additionally, the use of only one temperature reconstruction (for the northern hemispheric rather than global mean), underestimates the structural uncertainties in these estimates.
[79] There are additional issues concerning the analyses of Scafetta and West, even if the problematic parameter estimation for their models are ignored. One important difference between the solutions for 〈_{sun}〉(t) here and in SW06a can be traced to low S values in the work of Lean et al. [1995] reconstruction between 1970 and 1980. Using the more recent Lean [2000]S there is no trend since 1980. Furthermore, they spliced the ACRIM Total Solar Irradiance (TSI) product to a TSI reconstruction based on reconstruction by Lean et al. [1995] or Wang et al. [2005] in such a way that the average reconstructed TSI value over 1980–1991 corresponded with the ACRIM mean for the same period. However, the different series had different trends over the same period, and stitching together data in such a simple fashion is likely to introduce nonhomogeneity.
[80] A discrepancy between 〈_{sun}〉 (t) and the global mean temperature is clearly apparent in Figure 5, where the temperature exhibits a local maximum around 1940, whereas 〈_{sun}〉 (t) peaks around 1960 for all solutions. Similar characteristics can also be seen in the figures of SW06a, although they were not discussed.
[81] It has been also established that this 1890–1930 “early century warming” was limited to the Arctic [Johannessen et al., 2004] whereas the more recent warming has involved the whole latitudinal range. Thus a convincing solar warming hypothesis explaining both the warming periods would need to account for these different geographical fingerprints.
[82] Furthermore, SW06a did not carry out a proper trend analysis for estimating the increase in 〈T〉, but took the difference between instantaneous values of filtered data which also leads to a further inflation of their estimates. The purported lowend estimate of a 25% contribution from a solar origin since 1980 was not supported, as a proper trend analysis using a realistic reference level yields 8–10% when based on their strategy (Figure 5 and Table 7). If the Lean [2000]S were used instead of Lean et al. [1995], then the trend would be negative, thus more in line with Lean [2006].
Table 7. Trend Estimates (the Proportion of the Total Warming Explained) and Standard Deviation Derived Using a Linear Model Between T_{sun} and Year Since 1980, Expressed in the Percentage of Similar Trend Analysis for the GISS Temperature^{a}  Lean [2000]  SW06  “All years” 


Estimate  −7%  10%  8% 
Stdv  ±1.3%  ±1.3%  ±1.3% 
6. Conclusions
 Top of page
 Abstract
 1. Introduction
 2. Data
 3. Part 1: Multiple Linear Regressions
 4. Part 2: Scafetta and West Methodologies
 5. Discussion
 6. Conclusions
 Acknowledgments
 References
 Supporting Information
[84] We analyzed the GISS ModelE 〈T〉 in terms of its trend, LCF against solar forcing, and a set of regression analyses, and found that it gave a realistic reproduction of the observed global mean temperature. In particular, GISS ModelE simulates a response to solar and GHG forcings roughly consistent with the observations, but the exact contribution from each forcing is difficult to pinpoint using statistical methods alone. Linear regression does not give unbiased and robust results if one tries to attribute the effect of different forcings on the temperature. The lack of robustness can also give rise to inflated values for the coefficients used in the statistical models of Scafetta and West. Nevertheless, variations in S appear to have a weak effect on the global mean temperature, but cannot explain the global warming since 1980.
[85] We also repeated the analyses of Scafetta and West, together with a series of sensitivity tests to some of their arbitrary choices. These tests showed clearly that the published uncertainty in their estimates was greatly underestimated. In particular, the arbitrary assumption of their equilibrium sensitivity (Z_{eq}) has a dramatic impact on their attribution of 20th century changes to solar forcing. We next showed that their methodologies were not able to robustly retrieve the solar contribution in GCM experiments where the answer was known a priori. In fact, we found that the presence of internal variability and additional forcings greatly confounded their method's accuracy. Even in much simpler cases, examined here using Monte Carlo simulations of synthetic climate time series, we found that their diagnostics had a very wide range in the absence of a true signal, so cannot be considered robust metrics of a solarinduced contribution.
[86] We conclude that as with the simpler linear regression methodologies described earlier, the SW methodology is highly sensitive to the internal variability of the climate system and the presence of colinear trends in different forcings. Given the concomitant increases in greenhouse gas forcings over the 20th century, this implies that their published attributions greatly exaggerate the role of solar variations in global mean temperature trends.
[87] Claims that a substantial fraction of post 1980 trends can be attributed to solar variations are therefore without solid foundation, and solarrelated trends over the last century are unlikely to have been bigger than 0.1 to 0.2°C.