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1 doi: /nature10946 Supplementary figures and discussion (1) What are the radiative impacts of aerosols on shortwave radiation? Aerosols modify the distribution of radiative fluxes in the atmosphere. Anthropogenic aerosols thus exert a radiative forcing on the climate system, mainly in the solar, or shortwave, spectrum. Three distinct mechanisms are involved in the interaction between aerosols and radiation 28. First, aerosols absorb and scatter radiation: this is termed the direct radiative effect and it typically increases the amount of shortwave radiation reflected back to space at the top of the atmosphere and decreases the amount of shortwave radiation reaching the surface. Second, absorbed radiation within the aerosol layer causes a local warming that can suppress the formation of clouds and their reflection of shortwave radiation: this is the semi-direct radiative effect. Third, aerosols influence cloud microphysics by serving as cloud condensation nuclei in the formation of cloud droplets. Anthropogenic aerosols provide more cloud condensation nuclei therefore forming more and smaller cloud droplets for a given cloud liquid water content. More cloud droplets reflect a larger amount of shortwave radiation back to space: this is the first aerosol indirect forcing, exerted purely in the shortwave spectrum. Smaller cloud droplets take longer to reach precipitation sizes, thus increasing cloud lifetime and the associated reflection of shortwave radiation: this is the second aerosol indirect forcing. Note that only the semi-direct and second indirect forcings can be strong in the terrestrial, or longwave, spectrum. HadGEM2-ES includes direct, semi-direct, first and second indirect radiative effects of the main natural and anthropogenic aerosol species s7. For the year 2000, the globalaveraged direct radiative forcing exerted by anthropogenic aerosols in the shortwave spectrum is -0.3 Wm -2 at the top of the atmosphere and -0.9 Wm -2 at the surface. Those values are within the range given by the IPCC Fourth Assessment report. Corresponding numbers for the first indirect forcing are -1.3 and -1.5 Wm -2. Those values are at the stronger end of the (Intergovernmental Panel on Climate Change) IPCC range. Semi-direct and second indirect forcing modify cloud cover and thus cannot be quantified within the traditional (stratospheric adjusted) radiative forcing framework s8. It is however likely that the direct and first indirect components represent the bulk of the total shortwave aerosol radiative forcing. Aerosol direct effect and the associated semi-direct effect have been included in models contributing to the CMIP3 database. By contrast, aerosol indirect effects are a more recent addition and only a few CMIP3 models included those processes. As we show below these indirect effects have a crucial role in the evolution of Atlantic temperature changes. (2) Importance of indirect effects for surface shortwave radiation changes in the North Atlantic 1

2 Figure S1. Radiative forcing estimates for Direct and 1 st Indirect effects of aerosols in HadGEM2ES. Direct (left column), and indirect (right column) aerosol forcing quantified at 1950, 1980 and 2000 (top to bottom). To illustrate the importance of the indirect aerosol effects, we present the results of 3 simulations performed to quantify the direct and first indirect forcing at the surface in the North Atlantic. Radiative forcing is defined by IPCC 2007 as the change in net radiative fluxes exerted by a forcing agent, with surface and tropospheric temperatures and state held fixed at unperturbed values. We have set up HadGEM2- ES experiments where the forcing is diagnosed by calling the radiation scheme twice, with aerosol radiative effects included in the first call and not included in the second call. This configuration provides the aerosol forcing with respect to an atmosphere containing no aerosols. The aerosol forcing exerted by changes in aerosol concentrations since 1860 is then obtained by taking the difference with a parallel simulation where aerosol emissions are set to the year of interest: in the figure, 1950, 2

3 1980, or 2000 (figure S1). In those double call simulations, meteorology remains the same, independent of the aerosols included in the simulation (as dictated by the IPCC definition). Semi-direct and second indirect forcing involves changes in cloud cover, and cannot be quantified as described above. Given that the second indirect effect is likely to respond in a similar spatial and temporal pattern as the first indirect effect impact, we use the impact of the first indirect effect quantified here to be indicative of the larger overall indirect effect in HadGEM2-ES. The spatial pattern of direct forcing in each of the years (Figures 1a,c,e) shows strong correlation with the pattern of sulphate aerosol burden (main manuscript, figure 3) and is fairly homogeneously distributed across the North Atlantic region. The exception is the near equatorial region where increases in biomass-burning aerosols appear in 2000 as a band along the lower tropics. The spatial pattern of the 1 st indirect effect is more structured, and shares a common pattern for the 3 years studied. A region of stronger forcing extends across the northern part of the North Atlantic then branches down the east of the region off the coast of West Africa. This pattern matches the expected liquid cloud distribution, dominated by the North Atlantic storm track in the north and the predominance of stratocumulus cloud decks in the eastern Atlantic. This distribution of cloud remains largely robust through the late 19 th and 20 th centuries, with changes on multi-decadal timescales remaining small (~2%). So the climatological distribution of cloud determines the pattern and changes in aerosol burden determine the magnitude of the 1 st indirect forcing. In terms of magnitude over the North Atlantic, the 1 st indirect forcing is significantly stronger than the direct forcing in all years. 1 st indirect forcing represents more than 80% of the total aerosol forcing over ocean for the 3 years studied. Unlike the direct aerosol forcing of surface shortwave fluxes, which follows linearly changes in aerosol burden, the 1 st indirect forcing is stronger for aerosol increases over smaller background aerosol amounts (discussed with Figure 4, main manuscript). This behaviour derives from the cloud microphysics parametrisation, itself derived from aircraft observations, whereby cloud albedo varies logarithmically with cloud droplet number 3. Later increases in aerosol amounts exert proportionally weaker 1 st indirect effect forcing than earlier increases. The implication being that the relative magnitude of the 1 st indirect effect quantified for these three time periods (1950, 1980 and 2000) is likely to be similar or larger in the earlier historical period. The large magnitude of the aerosol 1 st indirect effect relative to the direct, illustrates the importance of indirect aerosol processes for shortwave changes in the North Atlantic, and points to why most CMIP3 models, which had yet to include indirect aerosol processes, underrepresented the forced temperature variability. The 2 nd indirect effect shares similar temporal and spatial structure to the 1 st indirect effect, and the radiative impact is of the same sign. The magnitude of the 2 nd indirect forcing can not be quantified within this same radiative framework. If it could be, it would lead to larger fraction of the total aerosol forcing being attributable to indirect effects. (3) Shortwave changes and the surface heat budget So far we have demonstrated the strong correlation between variability in shortwave changes and multi-decadal variability in SSTs. Figure S2 shows the historical changes in shortwave alongside the change in other surface fluxes. The heat budget presents fluxes into and out of the North Atlantic region mixed layer (as defined by a 3

4 temperature difference of 0.8 o C following the method in reference s9. As discussed in the main manuscript, the shortwave changes are closely coupled with the SST changes (Figure 2 in the main manuscript), and largely a forced response to changes in aerosol concentrations (Figure 4, main manuscript). The heat budget shows that multidecadal heat flux variability is dominated by the shortwave radiation (Figure S2c), and that through most of the historical period, shortwave radiation is the only flux to change with the sign required to drive the observed SST change. As we would expect to occur in response to such a large change in forcing, as the mixed layer rapidly warms/cools, the other fluxes adjust to bring the system back into equilibrium. Latent and sensible fluxes act to mitigate the external shortwave forcing, increasing in anti-phase with the shortwave changes as warmer (or cooler) SSTs lead to greater (or lesser) sensible and latent heat flux to the atmosphere. Given the importance of the overturning circulation in North Atlantic heat transport, it is likely that the advective and diffusive component of our heat budget contains a signal of changing ocean circulation. Indeed, these simulations show a near-linear increase in overturning circulation, but these changes act through a different mechanism (via freshwater rather than then heat fluxes). It is clear that advection change does not dominate the multidecadal variability here and therefore further discussion of the impact of changes in the overturning circulation are considered beyond the scope of this paper. A heat budget calculated for the simulation with aerosol emissions held constant (Figure S2 b and d), again shows the balance of large changes in heat fluxes into and out of the mixed layer, but lacks the coherent structure which results from the forced shortwave radiation change occurring in response to the time-varying aerosol emissions. The budget for the constant-aerosol simulations does show a suggestion of a weak multi-decadal signal, with small reduction in shortwave radiation post Krakatoa and Santa Maria Volcanic eruptions, and less obviously a weakening post Agung, El Chichong and Pinatubo. The degree of multidecadal variability captured by these volcanic signatures is significantly smaller than that exhibited in the standard historical simulations where aerosol changes are also included. 4

5 (4) Do the historical shortwave heat budget changes result directly from the radiative impacts of aerosols or mediated through dynamical ocean and hence SST changes? Figure S2. Mixed layer heat budget for the ensemble mean of simulations. Comparison of mixed layer heat budgets all available forcing data (a+c) and all forcing but aerosol emissions held at their year 1860 values (b+d). The top panels (a+b) demonstrate that changes within the mixed layer correspond to changes in SST over the same region ( W, N). All data presented in c and d has been smoothed using a 10 year running mean to clarify the signal from the noise. Data in parts a and b are presented as anomalies from the mean of the whole simulation, and in parts c and d, as an anomaly from the mean of the first 5 years of each variable (other than the derivative of the mixed layer temperature which presents absolute values), to highlight the divergence in fluxes. Longwave, shortwave, latent and sensible heat fluxes are calculated within and extracted directly from the model simulations. Advective and diffusive fluxes are the calculated as the closing term between the derivative of the annually averaged mixed layer temperature changes and the surface fluxes. Tests on simulations with all components of the heat budgets outputted explicitly by the model show this approach to be valid. The heat budget of the upper ocean points to historical changes in shortwave radiation as the component exhibiting the dominant multi-decadal variability. The absence of this variability when the historical aerosol emissions are omitted from a parallel set of simulations implicates aerosols as the prime driver (figure S2 c+d). There remains an open question, however, about whether these shortwave changes are the direct result 5

6 of the aerosol influence on atmospheric radiation balance or is somehow modulated or enhanced via dynamical changes in ocean circulation and SSTs which may drive shortwave via cloud changes. To address this question we repeat the simulation of the historical period, including an identical set of emission and concentration changes, but fixing the surface temperatures at 1860 values. This type of simulation provides information on how the radiation balance would have changed in the absence of any temperature, or dynamical feedbacks which may have occurred in the standard historical simulations. The shortwave radiation timeseries from this run is shown in Figure 2 (main manuscript) alongside the equivalent shortwave flux for the standard simulations. The similarity (in terms of phase and amplitude) between this run and the standard historical fluxes indicate that the historical shortwave changes during the historical period are largely externally forced (mainly by anthropogenic aerosols and volcanoes) rather than mediated via cloud distribution changes mediated through ocean and SST variability. (5) Taylor diagrams of CMIP3 simulations 6

7 Figure S3. Comparison of CMIP3 model and HadGEM2-ES historical SST simulations with observations. Models containing only direct aerosol effects are coloured red, those partially resolving indirect effects are shown in black, and those interactively resolving indirect as well as direct affects are coloured green. Prior to analysis all data (model and observations) have been smoothed with a 10 year running mean, so statistics represent model skill at replicating only the multidecadal component of variability. HadGEM2-ES is denoted by the circled triangle. Figure S3 shows the Taylor Diagram s10 comparison of climate model and ERSST observational estimate of multi-decadal variability in North Atlantic SSTs. This shows the normalised standard deviation (fraction of observed estimate) as the radial distance from the origin and the correlation with ERSST on the figure diameter. HadGEM2ES (circled) is placed closest to the observational reference point (at the 1.0, correlation 1.0 point) with normalised standard deviation of 0.75 and correlation of 0.65 (note the logarithmic axis) and the smallest centred Root Mean Square (RMS) error (concentric dotted circles around the Reference/ERSST point) of the collection of models. The other models plotted are the CMIP3 models discussed in the main manuscript (Figure 1). The simulations are colour code according to their representation of the 1 st indirect aerosol effect depending on whether it is not included (red), included but not fully interactive (black) or interactive (green) (table S2). Differences in Atlantic variability across this group of simulations is large, both in terms of correlation and standard deviations. A number of models represent aerosol 1 st indirect effects interactively. These include the CMIP3 model with the largest normalised standard deviation and the CMIP3 model with the largest correlation. However there doesn't not appear to be a strong clustering over all in the collection of models, with large spread in Atlantic variability within each composite. As discussed in the main manuscript, the details of implementation of aerosol indirect effects are also important. Quaas et al s11, 2009 show that amongst models contributing to the Aerosol Comparisons between Observations and Models (AEROCOM) intercomparison project, there is a wide range in the magnitude of aerosol responses between models. Of particularly interest here is model sensitivity of cloud albedo change to a change in aerosol amount in maritime regions (Quaas s11, Figure 2e). While some model representations (HadGEM2ES, some configurations of the National Center for Atmospheric Research, Community Atmosphere Model) reproduce the sensitivity of the satellite based estimate, other models significantly underestimate this magnitude (and hence the 1 st indirect effect) in these maritime regions. We'd expect therefore that differences in aerosol-cloud microphysics between models to contribute to a spread in the ability of models to reproduce forced historical variations in SSTs. The results in the main manuscript which show reproduction of multi-decadal variability in NASST, motivates the inclusion of aerosol indirect effects within Atlantic models, but the validation of the processes within those models is also important. 7

8 (6) Observational estimates of North Atlantic SST variability Figure S4. HadGEM2-ES and 5 different observational estimates of North Atlantic SSTs. HadGEM2-ES (orange) simulated North Atlantic SSTs (averaged over W, N) compared with five observational datasets s1-5 (black). One standard deviation of the model s ensemble spread is represented by the orange band. The trend for two periods is quoted in each panel, with error bounds based on 1 standard deviation of all trends between 5 years centred at the start of the period (either or ), and the 5 years centred at the end ( or respectively). The observations used in Figure 1 (main manuscript) were based on the ERSST dataset. There are a number of current ocean SST reconstructions, which all reproduce similar characterisation of the observed change in the North Atlantic. Five such datasets (ERSST, 3 rd Hadley Centre SST data set (HadSST3), Kaplan, Centennial in situ Observation-Based Estimates (COBE) and the Hadley Centre's sea ice and sea surface temperature data set (HadISST)) are illustrated in Figure S4 and compared against the HadGEM2ES simulations. Four of these reconstructions are spatially complete datasets (ERSST, Kaplan, COBE and HadISST) where gaps in the observational record are interpolated, and one (HadSST3) provides uninterpolated gridded data. Like Figure 1, main manuscript, uncertainty estimates (based on 1 standard deviation across the ensemble) are shown for HadGEM2-ES temperatures. The trends over two periods: warming between 1910 and 1940 and cooling between 1950 and 1975 are presented on the figure to provide a quantitative comparison between the different observational reconstructions 8

9 The observations all capture warming trends (1910 to 1940 and 1975 to 2000) and cooling trends (1950 to 1975). Differences emerge in the details, such as the decade where temperatures peaked or the magnitude of the trough. (7) Does the distribution of cloud also force or respond to the multi-decadal changes? Over the whole North Atlantic region, close similarities between the average historical shortwave changes and those from the forced run (Figure 4, main manuscript) point to external climate forcing driving much of the simulated shortwave change. Looking at smaller sub-regions there is a greater potential for feedbacks to play a role. In figure S5 we show the comparison of cloud amount in the average of the warm years minus cold years (warmest 3 rd of the data minus coldest 3 rd of the data, after the underlying trend has been removed). This extends the similar plots for differences in warm and cold averages calculated for aerosol burden, shortwave and temperature in Figure 3. Warm years are consistent with less cloud in the low cloud (stratus) region in the eastern North Atlantic, compared to cold years (Figure S5a), which show a stronger pattern of response compared to that expected from forced changes alone (Figure S5b) 9

10 Figure S5: Comparison of cloud response in fully coupled and forced responses. Difference between the average cloud fraction in warm years (warmest 3rd of all data) minus average of cold years (coldest 3rd of all data) after the timeseries has been detrended for a) the mean of the four coupled historical simulations and b) for the parallel simulation with fixed 1860 SSTs (where warm and cold years were used the same index as panel a). The temporal variability of the detrended data is compared c) between the full historical (coupled, black) and fixed SST (red) simulations, in a region encompassing the region of largest variability (red Focusing on the region with largest differences (stratocumulus cloud region off West Africa) the full historical and forced temporal variations share much of the same structure. Forced changes from other external climate drivers, such as greenhouse gases would also be expected to influence cloud amount, however, emergent temporal structure in the detrended timeseries (Figure S5c) points to an external forcing role with multi-decadal structure, such as aerosols (which change cloud fractions via the aerosol-cloud lifetime (2 nd indirect) effect). The larger response post 1950, in the full (coupled) historical runs points to a local role of temperature feedbacks not in the forced (fixed SST) simulation, a feedback which is documented in references s12 and s13. This temperature feedback on cloud amount is likely to locally enhance forced SW forcing in this region (Comparison of National Aeronautics and Space Administration s Earth Radiation Budget Experiment (ERBE) net cloud forcing observations with marine stratus clouds suggest that 0.01 difference in cloud fraction is consistent with roughly 1 W m -2 increase in net radiative balance s13 ). Returning to the wider context, over the North Atlantic region as a whole the forced changes in shortwave (arising from volcanoes and aerosols) closely track the simulated 10

11 shortwave changes in the fully coupled historical simulations (Figure 4, main manuscript). There are changes in cloud amount are consistent with changes in aerosol burden (Figure 3a) in the forced simulations, which illustrates a contributing from aerosol-cloud lifetime effects to the shortwave forcing. In localised areas there are regions where temperature feedbacks act to enhance this change. 11

12 (8) The role of dust changes in simulated multi-decadal variability.. Figure S6: Timeseries of monthly mean observed and simulated dust concentrations on Barbados. Timeseries are shown for a) the observations (from 1965 to 1998) taken from reference s6 and b) the monthly mean HadGEM2ES concentration, averaged over Barbados and the 8 surrounding grid boxes and the four historical simulations. Annual mean concentrations are over plotted (thick line) Changes in dust concentrations over the North Atlantic have been linked to changes in surface temperatures on short inter-year s14 and longer decadal timescales s15,16 during the satellite period. Comparatively, mineral dust plays a smaller role driving surface temperatures change in HadGEM2-ES where inclusion of mineral dust change increases the total variance NASST explained from 78% to 80%. HadGEM2-ES is unique in the CMIP5 generation of models in that it represents dust production interactively, as a function of vegetation fraction, soil moisture and winds. Comparison of HadGEM2-ES dust concentrations with one of the longest observational records s6 suggests that the climate model simulations, while capturing similar magnitude and inter-annual variability, do not capture common multi-decadal trends in dust suggested by the observed records (Figure S6). The lack a multi-decadal dust signal in the mean of the four HadGEM2-ES is due to the lack of a common coherent dust response across all four members, providing an explanation for why dust plays only a weak role in these simulations. Unlike the anthropogenic aerosols, changes in dust concentration represent a feedback to changing climate conditions in the important dust source regions. Drier conditions in the Sahel (linked to cool phases in Atlantic temperatures) lead to greater (and drier) bare soil, increasing wind driven erosion and subsequent transport over the Atlantic 12

13 region. HadGEM2-ES tends to over estimate bare soil extent in semi-arid regions 24 where the land surface aims to get the carbon balance right, at the expense of bare soil. There are many links from changing SSTs to the return transport of dust, which such an interactive dust model needs to get right, to capture the observed changes. The dust model in HadGEM2-ES is an important first step towards this, but does not yet capture observed multi-decadal trends. The Barbados timeseries for example (Figure S6a) shows larger concentrations during the 1970s and 1980s when cooler conditions in the Atlantic lead to wide spread Sahel drought. The absence of a similar signal in HadGEM2-ES suggests that these simulations are missing a potentially important feedback, the inclusion of which would act as a positive feedback on forced changes in the NASST. (9) Statistics used within this study. Figure S7. Comparison of simulated and statistically reconstructed SST changes using a range of explanatory variables. Ensemble mean modelled NASST (black) with no (solid) and 10 year (dashed) smoothing. Linearly modelled NASST using different combinations of forcing factors (green). The trends calculated in Table S1, quoted in Figure 1 (main manuscript) and Figure S4, represent the mean and standard deviation calculated from an ensemble of trends between all years between the quoted start date, plus and minus 2 years, and the end date, plus and minus 2 years (25 trend values in total). This approach represents a 13

14 more robust estimate of the underlying trend in both models and observed estimates, being less sensitive to inclusion or exclusion of individual years near either end of the period. The standard deviation of these trend estimates (provided in brackets in Table S1) provide an indication of the robustness of the individual trend estimates. Also indicated in bold in Table S1 are those model simulations which fall within the spread of trends calculated for the 5 observational datasets used in this study. The table also provides information on the normalised standard deviation and correlation relative to ERSST (statistics included in the Taylor diagram (Figure S3)) which are calculated from detrended data with a 10 year smoothing (emphasising multi-decadal component of the respective SSTs). The main manuscript quotes statistics on the variance of NASST explained by volcanoes, anthropogenic aerosols and mineral dust, both individually or combined. These statistics are based on the comparison of simulated (HadGEM2-ES) NASST variance and the variance of reconstructed NASST based on simple regression models. This model uses regression to relate NASST changes to explanatory variables, both detrended and smoothed with a 10 year filter to highlight the multidecadal component (Figure S7). NASST = β volcanic Optical volcanic + C NASST = β aerosol Optical aerosol + C NASST = β volcanic Optical volcanic + β aerosol Optical aerosol + C NASST = β volcanic Optical volcanic + β aerosol Optical aerosol + β dust Optical dust + C where β volcanic β aerosol and β dust represent regression coefficients, Optical volcanic Optical aerosol and Optical dust the respective optical depth changes and C the residual noise. The actual and reconstructed SSTS are all show in Figure S7. This illustrates the different contributions of volcanic and aerosol changes on the NASST. Formulated in this way, this simple model makes a simplification by explicitly assuming that the aerosol contribution to shortwave or SST changes is explained solely by optical depth changes. As is discussed in Figure 4b, main manuscript, the 1 st indirect effect shows more pronounced response to the early changes in aerosol amount than is indicated by the optical depth change (which corresponds to the direct aerosol effect). This is not accounted for within the regression framework presented above and the reconstructed NASST, therefore, provides a conservative estimation of the relative contribution arising from aerosol and volcanic changes. Within the text of the main manuscript we show the shortwave radiation entering the surface ocean to vary in phase with SST change, and variability in the volcanic and anthropogenic aerosol optical depths (Figure 2). We then go on to demonstrate that the variability in shortwave radiation is a forced response to external factors, and largely to aerosol emission, transport over the Atlantic, and interaction with cloud microphysics (Figures 3 and 4). We do not have simulations however which allow us to account separately for the relative contribution of the two main drivers of shortwave change, volcanic and anthropogenic aerosol concentrations, throughout the whole of the historical period. To examine this with the data available, we can explore the relative contributions of volcanic and anthropogenic aerosol concentrations on changes in shortwave radiation by finding the best fit (by means of the least-squares approach) single and multiple linear regression models relating the various components. We do this taking volcanic aerosol and anthropogenic aerosol optical 14

15 depth separately and together as explanatory variables. The reconstructed shortwave radiation from each model, and the shortwave radiation simulated interactively within the full HadGEM2-ES simulations are shown in figure S8. From these regression models we can calculate the proportion of the total variance described by the Earth System Model's shortwave radiation, accounted for by each variable separately and together. We find that 79%, 48% and 36% of the variance is explained respectively by utilising both the volcanic and aerosol optical depths, just the anthropogenic aerosol optical depths, and only the volcanic aerosol optical depths. In this analysis we take absolute aerosol optical depths as the explanatory variables, rather than making any inference about how the aerosols are interacting with the radiation (direct/indirect effects), and using (for example) the exponent of the optical depth as Beer's law would suggest if we were considering the first indirect aerosol effect alone. Figure S8: Comparison of simulated North Atlantic shortwave changes with statistically reconstruction based on different explanatory variables. Ensemble mean shortwave radiation (SW) entering ocean (black line), linear model estimating the shortwave radiation intensity from modeled total anthropogenic aerosol optical depth and volcanic index (green, solid), anthropogenic aerosols only (green, longdash), and volcanic emissions only (green, short dash). Linear models explain 79%, 48% and 36% of the variance respectively. 15

16 Supplementary Tables Table S1: Summary statistics 20 th Century Trends (std. dev.) Detrended statistics CMIP to to to 1998 Correlation Normalised Standard dev. GFDL CM (0.02) (0.04) 0.22 (0.04) GFDL CM (0.02) (0.02) 0.27 (0.03) GISS E H 0.18 (0.00) (0.02) 0.15 (0.03) GISS E R 0.14 (0.00) (0.03) 0.15 (0.02) MIROC 3.2 (medres) 0.06 (0.02) (0.02) 0.08 (0.05) MIUB ECHO-G 0.22 (0.02) (0.02) 0.22 (0.04) MRI CGCM2.3.2a 0.15 (0.01) 0.05 (0.03) 0.35 (0.02) NCAR CCSM (0.01) 0.02 (0.02) 0.22 (0.04) NCAR PCM (0.01) (0.04) 0.26 (0.02) UKMO HadCM (0.02) (0.06) 0.27 (0.02) UKMO HadGEM (0.02) (0.08) 0.15 (0.07) CMIP5 UKMO 0.32 (0.03) (0.08) 0.32 (0.04) HadGEM2ES Observations ERSST 0.82 (0.04) (0.07) 0.26 (0.09) KAPLAN 0.61 (0.06) (0.06) 0.35 (0.08) HadSST (0.04) (0.06) 0.39 (0.08) COBE 0.65 (0.02) (0.07) 0.32 (0.09) HadISST 0.67 (0.07) (0.08) 0.31 (0.10) This table shows estimates of the mean trends (and standard deviations of this estimate) for 3 periods (1910 to 1940, 1950 to 1975 and 1975 to 1999). These values highlighted in bold lie within the distribution of trends calculated from the observational datasets. The table also presented the correlation to ERSST and the normalised standard deviations (relative to the standard deviation of ERSST). Details of these statistics are given in the supplementary discussion above. 16

17 Table S2: Contributing models Model Ensemble 1 st Indirect 2 nd Indirect Ensemble size GFDL 2.0 ENS2 none none 3 GFDL 2.1 ENS1 & ENS2 none none 3 GISS EH ENS1 & ENS2 offline offline 5 GISS ER ENS1 & ENS2 offline offline 7 ECHO-G ENS2 interactive none 5 MIROC ENS2 interactive interactive 3 MRI ENS1 & ENS2 none none 5 NCAR CCSM ENS1 & ENS2 none none 8 NCAR PCM ENS1 & ENS2 none none 4 HadCM3 ENS2 offline none 4 HadGEM1 ENS2 interactive interactive 3 HadGEM2-ES - interactive interactive 4 The table shows the models contributing to the two previous multi-model ensembles, marked either as ENS2 (for those only in reference 9) or both. The representation of indirect effects in each models is indicated as none, offline (for models which use online estimates) or interactive (where the indirect effect is modelled interactively) and the number of ensemble members for each model used in this study is given in the last column. 17

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