Response of Earth s surface temperature to radiative forcing over A.D

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 116,, doi: /2010jd015143, 2011 Response of Earth s surface temperature to radiative forcing over A.D A. D. Friend 1 Received 4 October 2010; revised 5 April 2011; accepted 12 April 2011; published 15 July [1] An energy balance model (EBM) of the annual global mean surface temperature is described and calibrated to the sensitivity and temporal dynamics of the Goddard Institute for Space Studies modele global climate model (GCM). The effective radiative forcings of 10 agents are estimated over the past 2009 years and used as inputs to the model. Temperatures are relatively stable from around A.D. 300 until a Medieval Climate Anomaly starting around A.D This is ended by a massive volcanic eruption in A.D. 1258, which initiates a multicentury era of low and relatively variable global mean temperatures, including a Little Ice Age A.D This era only ends at the beginning of the 20th century. The model estimate of forced centennial variability is smaller than the observed variability in reconstructions over the past two millennia. Also, the default parameterization results in less warming than observed over A.D Prediction uncertainty in the pre industrial era is dominated by solar forcing, with the climate feedback factor and volcanic aerosols also playing important roles. In contrast, prediction uncertainty post A.D is much higher and dominated by uncertainties in direct and indirect aerosol and land use forcings. Improving estimates of these will greatly increase our ability to attribute observed temperature variability to contemporary forcings. Citation: Friend, A. D. (2011), Response of Earth s surface temperature to radiative forcing over A.D , J. Geophys. Res., 116,, doi: /2010jd Introduction [2] Understanding current warming trends on Earth require that we separate the impacts of anthropogenic forcings from those of natural factors such as solar variability and massive volcanic eruptions [Hegerl et al., 2007]. Energy balance models (EBMs) enable rapid and tractable assessments of these roles as well as analysis of uncertainty arising from imperfect knowledge of forcings and system sensitivity, with the latter potentially prescribed from more complex models such as global climate models (GCMs). Furthermore, EBMs can be developed into simple Earth system models through the inclusion of biogeochemical parameterizations, and be used thereby to improve understanding of coupled feedbacks. [3] This paper describes a new simple EBM and the development of a comprehensive mean annual radiative forcing data set consisting of ten agents over the past 2009 years. The EBM is calibrated to the global mean behavior of a GCM and predicted annual variability in global mean surface temperature is compared to reconstructions and the instrumental record. An uncertainty analysis is performed to determine the relative importance of the uncertainty in different forcings and model parameters for model prediction. 2. Energy Balance Model [4] An EBM is used here to calculate the evolution of Earth s global mean surface temperature in response to changing radiative forcing, and is based on the analysis of Hansen et al. [1984] (hereinafter H84). H84 separate the equilibrium surface temperature response to a change in solar forcing into a component that restores radiative equilibrium with space and a component that results from internal system feedbacks such as changes in the vertical atmospheric temperature structure, water vapor, ground albedo, and clouds DT eq ¼ f DT o ; where DT eq is the change in surface temperature required to restore radiative equilibrium following a change in solar irradiance, DT o is the change in equilibrium surface temperature in the absence of feedbacks, and f is the net feedback factor due to feedbacks initiated by changes in solar irradiance (dimensionless). DT o is the same as the change in the effective radiating temperature of Earth, T e. At equilibrium this effective temperature is that which balances absorbed total solar radiation with longwave energy loss to space, and therefore T e is given by (H84) ð1þ T e ¼ ½S o ð1 AÞ= ð4þš 1=4 ¼ ðs=þ 1=4 ; ð2þ 1 Department of Geography, University of Cambridge, Cambridge, UK. Copyright 2011 by the American Geophysical Union /11/2010JD where S o is solar irradiance, A is Earth s albedo, s is the mean flux of absorbed radiation per unit area, and s is the Stefan Boltzmann constant. H84 used this relationship between 1of15

2 radiative temperature and absorbed solar radiation to derive the rate of change in effective temperature with change in forcing dt e ¼ 1 ds o ¼ 1 ds T e 4 S o 4 s : [5] Therefore the relative change in the effective temperature equals 0.25 the relative change in solar forcing. This framework is extended here to include the response of Earth s surface temperature to changes in greenhouse gas mixing ratios as well as solar irradiance and thereby to other nonsolar forcings. [6] If there were no feedbacks, following a sufficient length of time after a change in the mixing ratio of a greenhouse gas the global mean surface temperature would reach an equilibrium temperature analogous to T o (T o,g ). If feedbacks are treated as for the response to solar irradiance, then the total change in surface temperature at equilibrium due to changed mixing ratio of a greenhouse gas (T eq,g ) is given by DT eq;g ¼ f g DT o;g ; where f g is the net feedback factor due to feedbacks initiated by changes in greenhouse gas mixing ratios (dimensionless). [7] Using a GCM, H84 computed that the global mean equilibrium surface temperature response to a +2% change in solar irradiance or a doubling of atmospheric CO 2 is very similar (i.e., 4 C). In these experiments, a 2% increase in solar irradiance corresponded to a radiative forcing at the tropopause of +4.8 W m 2, and a doubling of CO 2 corresponded to a global mean forcing of about 4 W m 2, with peak flux into the ocean surface of 4 5 Wm 2 in both experiments. This similarity between surface temperature responses to both solar and greenhouse gas forcings is used here to extend the description of the solar response given above to also include nonsolar forcings. Applying the relationship between solar forcing and surface temperature given in equation (3) to nonsolar forcings does not mean to imply that the model assumes that the physics of the system responds the same to all forcings, but rather that the magnitude and functional form of the relationship is similar. [8] The EBM accounts for the response of the equilibrium Earth radiative temperature to solar forcing using (3). The similarity between the response to solar and greenhouse gas forcings is used to justify extending this equation to calculate the equilibrium surface temperature response to simultaneous solar and nonsolar forcings in the absence of feedbacks (T o,sf ) dt o;sf T e ¼ 1 4 ð3þ ð4þ ðds þ ddfðghgþþ ; ð5þ s where DF(GHG) is nonsolar forcing. The change in the total equilibrium surface temperature in response to solar and nonsolar forcings, T eq,sf, is then calculated using the net feedback factor as in equation (4), DT eq;sf ¼ f g DT o;sf : [9] All changes in the physical components of the Earth system that result in feedbacks, such as atmospheric water ð6þ vapor, surface albedo, and cloud height, are subsumed into the net feedback factor. [10] In the EBM, changes in T e in response to changes in solar irradiance, and changes in T o,sg in response to total forcing both occur with relationships conditioned on T e /(4s), and total surface temperature changes result from the amplification of T o,sg by the net feedback factor (equation (6)). This construction reproduces the equilibrium global mean surface temperature responses to solar and CO 2 forcings simulated in H84. [11] As indicated, H84 found that the radiative forcing from doubled CO 2 is lower than from +2% solar irradiance. However this was more than compensated by a higher feedback factor associated with changes in CO 2 (i.e., f g =3.45 compared with f = 2.96). Therefore, when all feedbacks are considered, the equilibrium global mean surface temperature increased slightly more with doubled CO 2 (i.e., +4.2 C) than it did with increased solar irradiance (i.e., +4.0 C). This difference in the magnitude of the surface temperature response to different forcings is incorporated into the EBM through the use of forcing efficacies, as described below. The different feedback factors suggested by the results of H84 are not incorporated into the formulation explicitly. However, f g f = 0.49 is well within the range of parameter values used in the uncertainty analysis (see below). [12] Taking A = 0.31 and S o = W m 2, Earth s radiative temperature, T e, is initially taken to be K in the simulations described below. This value of S o used here is lower than that assumed by H84, and results from improved observations made by the TIM instrument flying on the SORCE, and is taken as the solar minimum reported by Kopp et al. [2005]. Surface temperature is initially assumed to be at its equilibrium value, taken to be 33 K higher than T e (i.e., K) (H84). [13] The default value for the net feedback factor is calculated from the sensitivity of the model III version of the NASA Goddard Institute for Space Studies (GISS) modele GCM as reported by Hansen et al. [2005] (hereinafter H05). This model is described by Schmidt et al. [2006]. The GCM equilibrium global mean surface temperature sensitivity to doubled CO 2 from 291 ppm is 2.7 C (H05). The effective (see below) global mean radiative forcing due to doubled CO 2 in this model is 4.22 W m 2, which yields DT o = 1.14 K, and therefore f g (= f ) = 2.7/1.13 = [14] Global mean surface temperature is assumed to continually decay towards T eq,sg, with temporal dynamics calibrated to the simulation results of the GISS modele GCM. H05 investigated the sensitivity and dynamical responses of the GCM to doubled CO 2 using alternative ocean representations. The mean of ensemble GCM simulations minus their controls obtained using a 300 yr doubled CO 2 GCM experiment with the coupled dynamical ocean of Russell et al. [1995] is used here (Figure 1). [15] The GCM surface temperature dynamical response could not be captured with a single heat capacity. The simplest approximation that retains sufficient skill is to assume three components to the temperature response: fast, medium, and slow. Assuming these three components of the thermal response scale by orders of magnitude, their e folding times are therefore related to one another by 100 f ¼ 10 m ¼ sl ; ð7þ 2of15

3 Figure 1. Global mean surface temperature response to doubled CO 2 simulated by the GISS modele GCM (H05) (black lines) and by the EBM calibrated to the GCM result using three heat components and f g = 2.37 as described in the main text (solid red line). Seventy percent of the equilibrium warming response occurs within 100 years. where t f, t m, and t sl are the e folding times of the fast, medium, and slow components, respectively. This construction is not intended to have any direct physical significance, although the three thermal components might notionally correspond to the land and ocean surface, ocean mixed layer, and the deep ocean. The intention is simply to fit the GCM results, and could easily be reparameterized to fit other GCMs. [16] Each contributing component is assumed to decay towards T eq,sf according to dt i dt ¼ T i T eq;sf =i ; ð8þ where T i is the contribution to the surface temperature from component i such that T s ¼ T f þ T m þ T sl ; where a, b, and g are the fractions of the total thermal response due to the respective components (i.e. a + b + g =1), and t i is the e folding time of component i. An excellent fit to the GCM is obtained with t f = 2 yr, a =0.4,andb =0.16 (Figure 1), and these values are taken as default parameterizations in the simulations presented here. 3. Radiative Forcings [17] The annual global mean radiative forcings due to the well mixed anthropogenic greenhouse gases CO 2,CH 4,N 2 O, and CFC type halogenated compounds, ozone (O 3 ), CH 4 derived stratospheric water vapor, solar irradiance, land use, changes in snow and ice albedo due to deposition of black carbon (BC), stratospheric aerosols of volcanic origin, tropospheric BC, and the direct and indirect effects of reflective aerosols are estimated here for A.D [18] Forcings vary in their effectiveness at producing global surface temperature change, due primarily to spatial variability. It is therefore more relevant to calculate an effective forcing for input to an EBM such as used here. Effective forcing, Fe (W m 2 ), is defined by H05 as Fe ¼ EaFa ¼ DT s =; ð9þ ð10þ where Ea is the efficacy of the forcing agent, Fa is the adjusted forcing, DT s is the equilibrium global temperature change, and g is the equilibrium climate sensitivity to CO 2 forcing ( C per W m 2 ). The concept can also be usefully applied to nonequilibrium conditions, as long as the standard response is carefully quantified. Effective forcing is then the radiative forcing by CO 2 that would cause the same global mean surface temperature change after the same time period, and Ea therefore depends on the time period considered for adjustment of surface temperature. Adjusted forcing, Fa, is the forcing after the stratospheric temperature has been allowed to adjust to the perturbation and is the standard forcing employed by the Intergovernmental Panel on Climate Change (IPCC) [2001]. [19] H05 used the GISS modele GCM to compute the global mean surface temperature response to a standard CO 2 forcing against which to measure the efficacies of other forcing agents at producing surface temperature change. This standard forcing response was computed as the global mean surface temperature change resulting from a 1.5 increase in CO 2 mixing ratio from the A.D value of 291 ppm, computed over model years Surface temperature increased by C and Fa was computed to be 2.39 W m 2 when using the WMO tropopause definition, and 2.37 W m 2 for a fixed pressure height definition (H05), giving DT s /Fa = g C (W m 2 ) 1. Transient effective forcings were calculated relative to this value by Hansen et al. [2007] (hereinafter H07) and M. Sato and J. Hansen (Global Mean Effective Forcing, accessed 10 June 2010, (hereinafter Sato and Hansen, online data set, 2010), and are used here to derive estimates of all ten forcings over A.D as described in subsequent sections Atmospheric CO CO 2 Radiative Forcing [20] The GISS modele GCM simulation results reported by H05 are used here to compute the effective annual global mean radiative forcing by CO 2 over A.D from estimates of changes in annual mean atmospheric CO 2 mixing ratio. H05 computed the effective radiative forcing of a wide range of CO 2 mixing ratios relative to an unperturbed state computed using a value of 291 ppm (i.e. its value in A.D. 1880) (Figure 2a). A range of simplified expressions for the dependency of global mean forcing on CO 2 mixing ratio are given by IPCC [2001, Table 6.2], and the best fit to the simulations of H05 is obtained here with fitted coefficients to FeðCO 2 Þ ¼ lnðc=c o Þþð p C p C o Þ; ð11þ where C is the varying CO 2 mixing ratio (ppm) and C o is its unperturbed value. Fitted coefficients are a = and b = , and the fitted relationship is shown in Figure 2a together with the GCM simulation results. Fitting was achieved by minimizing the sum of the squares of the errors, and this fitting technique is used throughout this paper unless otherwise stated. [21] The adjusted forcing by CO 2 (i.e. Fa(CO 2 )) reported by H05 is also shown on Figure 2a, and is close to Fe(CO 2 ) up to 1000 ppm, above which Fe(CO 2 ) increases discernibly faster than Fa(CO 2 ). Fitted coefficients for Fa(CO 2 ) are a = and b = This divergence reflects the 3of15

4 Figure 2. Relationships between estimated global mean radiative forcings and mixing ratios of wellmixed greenhouse gases. (a) CO 2. Red squares are the simulated effective forcings from H05 computed using the GISS modele CGM relative to the forcing at an unperturbed mixing ratio of 291 ppm, and the red line is the fit to these using equation (11) (coefficients are given in the text). Blue crosses and lines are the same but for adjusted forcings. Also shown is the relation of Myhre et al. [1998] (black line) (i.e., 5.35 ln(c/c o )), originally cited as valid <1000 ppmv [Shine et al., 1990], with the original functional form from Wigley [1987]. (b) CH 4. Colored lines and symbols as in Figure 2a relative to an unperturbed mixing ratio of 837 ppb (N o = 278 ppb) and with fits using equation (14) (coefficients are given in the text). Symbols at 1750 ppb are values reported by H05 for A.D adjusted to A.D forcings by subtracting the fitted A.D forcing. Black line is the relation of Myhre et al. [1998], originally from Shine et al. [1990] and based on work by Wigley [1987] and Hansen et al. [1988], cited by Shine et al. [1990] as valid <5 ppmv. (c) N 2 O. Lines and symbols as for CH 4. (d) CFC 11 + CFC12 (1:2 mixing ratios). Black line is relation of Myhre et al. [1998]. Symbols are simulation results of H05, and lines are fits to these using equation (15). increasing efficacy of CO 2 in producing surface temperature change as its mixing ratio increases, and is the result of the increasing strength of climate feedbacks, such as the water vapor feedback, with forcing (H05). It needs to be borne in mind that because the relative importance of different feedbacks is time scale dependent, the details of the relationships derived from the GCM are to some extent dependent on the time scale used (H05 calculated a 100 year response). Also shown on Figure 2a is a commonly used estimate of radiative forcing by CO 2 [Myhre et al.,1998],computedrelativeto 291 ppm. At 400 ppm, Fe(CO 2 ) is 10.2% greater than the estimate of Myhre et al. [1998] (see inset) and therefore, given the importance of CO 2 as a climate forcing on decadal and greater time scales, this difference will likely have implications for the attribution of surface temperature to forcing agents, as well as predictions of future impacts of rising CO CO 2 Mixing Ratios [22] Annual global mean tropospheric CO 2 mixing ratios for A.D are constructed from ice core measurements and for A.D from atmospheric measurements. [23] Measurements made on the ice and firn collected at Law Dome in Antarctica [MacFarling Meure et al., 2006] are used to calculate global mean values over A.D using a derived relationship with fossil CO 2 emissions. The latitudinal gradient in atmospheric CO 2 is changing with time as fossil CO 2, of primarily northern hemispheric origin, is superimposed on the natural gradient. The difference between the global mean CO 2 mixing ratio and the value measured in the Law Dome ice core is assumed to increase linearly with the rate of fossil CO 2 emissions, following Taylor and Orr [2000], D ¼ f CO2 þ ; ð12þ where c D (ppm) is the global mean South Pole surface CO 2 mixing ratio difference (ppm), f CO2 is the rate of fossil CO 2 emissions (Pg C yr 1 ), a is the sensitivity of the difference to the flux of fossil CO 2 (ppm (Pg C yr 1 ) 1 ), and b is the difference under conditions of no fossil CO 2 (ppm). b represents the effect of the natural component of the latitudinal CO 2 gradient, and is assumed constant in time (but see Taylor and Orr [2000] for arguments why some variation might be expected). [24] The coefficients in equation (12) are derived here using the relationships between the globally averaged 4of15

5 Figure 3. Relationships used to estimate quantities outside the range of previous estimates. (a) Relationship between fossil CO 2 emissions and human population, A.D (crosses). Red line is fit using equation (13). (b) Relationship between the global mean South Pole CO 2 mixing ratio difference and the rate of fossil CO 2 emissions, A.D (crosses). Red line is fit using equation (12) (coefficients given in the main text). (c) Relationship between the global mean South Pole CH 4 mixing ratio difference and the rate of fossil CO 2 emissions, A.D , and linear fit using equation (12) (coefficients given in the main text). (d) Relationship between land use related CO 2 emissions and human population, A.D , and linear fit. (e) Relationship between O 3 forcing computed by H07 and total C emissions, A.D (f) Relationship between land use forcing computed by H07 and land use related CO 2 emissions, A.D , and linear fit. (g) Relationships between forcings due to black carbon, snow albedo, reflective aerosols, and the aerosol indirect effect computed by H07 and fossil CO 2 emissions, A.D (h) Relationships between forcings due to black carbon, snow albedo, reflective aerosols, and the aerosol indirect effect computed by H07 and fossil CO 2 emissions, A.D (R 2 = for all regressions). 5of15

6 Figure 4. Estimated annual global mean mixing ratios of well mixed greenhouse gases (lines) and measurements used to derive the global means (symbols). (a) Estimated annual global mean atmospheric CO 2 mixing ratio, A.D Also shown are the ice core measurements from MacFarling Meure et al. [2006], A.D (diamonds), and global estimates of mixing ratios from the direct measurements of Tans [2010], A.D (crosses). (b) Estimated annual global mean atmospheric CH 4 mixing ratio, A.D (red line), ice core measurements from MacFarling Meure et al. [2006], A.D (diamonds), and global mean estimates from the combined ice core and atmospheric measurements of Hansen and Sato [2004], A.D (crosses), with additional estimate for A.D (cross). (c) Estimates and measurements of global mean annual N 2 O mixing ratios as for CH 4, but with linear smoothing over A.D between the global mean estimates based on the two ice core records. (d) MPTGs and OTGs. The omtpgs are MPTGs excluding CFC 11 and CFC 12. No observations for CH 3 Br prior to A.D. 1992; hence values during that period are estimated as CCl 4 /11.8 (their ratio in A.D. 1992) as CCl 4 declines at a similar rate to CH 3 Br over A.D CF 4 is linearly scaled back from its measured value of 40 ppt in A.D to an assumed preindustrial value of 34 ppt (see main text). marine surface annual mean CO 2 mixing ratio of the NOAA Earth System Research Laboratory [Tans, 2010], the annual mean flask air measurements of CO 2 mixing ratio at the South Pole by the Scripps Institution of Oceanography [Keeling et al., 2008], and the global sum of fossil fuel burning, cement manufacturing, and gas flaring related CO 2 emissions taken from Boden et al. [2010], with emissions for A.D and A.D taken from BP (BP Statistical Review of World Energy, categoryid=6929&contentid= ) and values prior to A.D estimated from global human population as follows. [25] Global mean annual human population for A.D is derived here as a linear interpolation of the lower estimates of the compilation summary of U.S. Census Bureau, Population Division [2010a], and merged with annual values for A.D from U.S. Census Bureau, Population Division [2010b]. Both human population and fossil CO 2 emissions increase exponentially from about A.D. 1750, but the greater rate of increase in emissions than population results in an exponential relationship between the two (Figure 3a). An exponential equation is fitted between the fossil CO 2 emissions and human population over A.D (a strong discontinuity in emissions occurs in A.D. 1830), with the following providing an excellent fit: f CO2 ¼ ð0:43pþ 4:7 ; ð13þ where P is human population (10 9 ) (Figure 3a). [26] The relationship between c D and f CO2 over A.D , the years when the three data sets coincide, is shown in Figure 3b. A best fit linear regression of equation (12) to this relationship is obtained with a = ppm (Pg C yr 1 ) 1 and b = ppm (Figure 3b). [27] The Law Dome ice core measurements of MacFarling Meure et al. [2006] are here linearly interpolated to annual values and, together with the annual fossil CO 2 emissions and equation (12), are used to estimate global mean CO 2 mixing ratios for A.D The resulting value for A.D is ppm. The ice core derived and direct atmospheric measurement derived estimates of Tans [2010] are merged to produce a complete A.D annual time series of global mean atmospheric CO 2 mixing ratios (Figure 4a). [28] These mixing ratios, together with equation (11) parameterized as described above, yield an effective forcing of 1.92 W m 2 over A.D (1.65 W m 2 over A.D. 6of15

7 Table 1. Effective Radiative Forcings (W m 2 ) due to Different Agents a Years A.D. CO 2 CH 4 N 2 O MPTGs+OTGs Solar Ozone Stratospheric Water Land Use Snow Albedo Black Carbon Reflective Aerosols AIE Net a Net is sum (actual net used in simulations 0.89 this value) ) (Table 1 and Figure 5a). IPCC [2001] presented a value of 1.46 W m 2 for the adjusted CO 2 forcing over A.D , whereas the value calculated here is 1.67 W m 2, 14.4% higher Atmospheric CH CH 4 Radiative Forcing [29] The simplified expression for the direct forcing due to CH 4 given in Table 6.2 of IPCC [2001] is fitted here to the values computed by H05 (Figure 2b). This expression includes dependencies on both CH 4 and N 2 O mixing ratios FeðCH 4 Þ ¼ að p M p M o Þ ðfðm; N o Þ fðm o ; N o ÞÞ; ð14þ where M is the CH 4 mixing ratio (ppb), M o and N o are the unperturbed mixing ratios of CH 4 and N 2 O, and f(m, N) = b ln[ (MN) M(MN) 1.52 ], where N is the N 2 O mixing ratio (ppb). H05 computed Fe(CH 4 ) for two large changes in mixing ratio from A.D values, but one is larger than the valid range of equation (14) [Shine et al., 1990]. Therefore, to further constrain the relationship at lower mixing ratios, a value of Fe(CH 4 ) = 0.58 W m 2 for A.D is included in the regression, estimated from Figure 28 of H05. Equation (14) is then fitted to these two values, giving a = and b = 4.50 (Figure 2b). It proved impossible to improve the fit by changing any of the other coefficients. The resulting forcings are compared with those reported by IPCC [2001] in Figure 2b, together with the simulated and estimated values of Fa(CH 4 ) (fitted regression coefficients for Fa(CH 4 ) are a = and b = 3.18). [30] The efficacy of CH 4 at producing surface temperature change is substantially greater than 100%, and therefore Fe(CH 4 ) increases faster with mixing ratio than Fa(CH 4 ). IPCC [2001] report a forcing of 0.48 W m 2 over A.D , whereas H05 computed an adjusted direct forcing of 0.55 W m 2, 15% greater. This difference increases to 21% when comparing the effective forcing from H05 with the IPCC [2001] value CH 4 Mixing Ratios [31] Annual global mean atmospheric CH 4 mixing ratios for A.D are estimated in a similar manner to CO 2. Values for A.D are taken directly from J. Hansen and M. Sato (Global Mean CH 4 Mixing Ratios, accessed 31 May 2010, Fig1B.ext.txt), which were derived from ice core and atmospheric measurements using methodology described by Hansen and Sato [2004]. A value for A.D is estimated by adding the A.D change to the A.D value. [32] Pre A.D values are calculated from measurements made in the same ice core as used for CO 2 [i.e., MacFarling Meure et al., 2006]. These measurements are first interpolated to annual values, and annual differences Figure 5. Estimated radiative forcings due to (a) CO 2, (b) CH 4, (c) N 2 O, and (d) MPTGs+OTGs, A.D Global mean mixing ratios as in Figure 4. 7of15

8 with the global values calculated for A.D These values are then regressed against fossil CO 2 emissions, and the relationship fitted using equation (12), yielding a = 5.39 ppb (Pg C yr 1 ) and b = 15.4 ppb (Figure 3c). Pre A.D values are then obtained by adding the annual global South Pole differences predicted from fossil CO 2 emissions by equation (12) to the interpolated ice core measurements. These ice core derived and direct atmospheric measurement derived estimates are then merged to produce a complete A.D time series of global mean atmospheric CH 4 mixing ratios (Figure 4b). [33] Comparing different ice core records, Chappellaz et al. [1997] found that the Greenland to Antarctica CH 4 gradient varied between 33 and 50 ppb over the Holocene due to changing roles of the tropics and boreal regions as sources. Most of the current gradient of about 140 ppb is in the Northern Hemisphere, and so if this were also true in preindustrial conditions it would be consistent with the global mean South Pole difference of 15 ppb calculated here. [34] These estimated global mean CH 4 mixing ratios, together with equation (14), yield Fe(CH 4 ) = 0.63 W m 2 over A.D (0.60 W m 2 over A.D ) (Table 1 and Figure 5b). CH 4 adjusted forcing calculated here is 0.55 W m 2 over A.D , 14.6% higher than the value reported by IPCC [2001]. CH 4 also has indirect effects through stratospheric H 2 O and, especially, tropospheric ozone (O 3 ); these are separately estimated below Atmospheric N 2 O N 2 O Radiative Forcing [35] H05 computed the effective radiative forcing due to the N 2 O mixing ratio change ppb. They also computed Fa(N 2 O) = 0.15 W m 2 for ppb, which gives Fe(N 2 O) = 0.16 W m 2, assuming the value of Ea (1.04) computed for the greater change. The resulting two values of Fe(N 2 O) are here fitted to equation (14), but with M and N swapped, yielding a =0.0573(b is kept to the same value as for CH 4 ), and the result is shown in Figure 2c. Also shown are the curves for Fa(N 2 O) derived as for Fe(N 2 O) (a = ) and that reported by IPCC [2001]. [36] The three estimates are very similar around contemporary mixing ratios (inset), but the H05 derived values increase noticeably more rapidly with mixing ratios above 0.5 ppm N 2 O Mixing Ratios [37] Global mean atmospheric N 2 O mixing ratios for A.D are taken directly from J. Hansen and M. Sato (Global Mean N 2 O Mixing Ratios, accessed 1 June 2010, which were derived from ice core and atmospheric measurements using methodology described by Hansen and Sato [2004]. A value for A.D is estimated by adding the A.D change to the A.D value. Earlier values are taken directly from the (interpolated) ice core record of MacFarling Meure et al. [2006], but with linear smoothing between the two records over A.D The resulting complete time series is shown in Figure 4c which, together with equation (14), yields an effective forcing of 0.20 W m 2 over A.D (0.16 W m 2 over A.D ) (Table 1 and Figure 5c). The estimate of radiative forcing by N 2 O using the relation of IPCC [2001] is almost identical to that computed here (Figure 5c) Montreal Protocol Trace Gases and Other Trace Gases Radiative Forcing by MPTGs+OTGs [38] Radiative forcings of the Montreal Protocol trace gases (MPTGs) and other trace gases (OTGs) are calculated using the expression given in Table 6.2 of IPCC [2001], FaðCFCsÞ ¼ ðx X o Þ; ð15þ where X is the changing mixing ratio (ppb), X o is the unperturbed mixing ratio (ppb), and a is a constant (W m 2 ppb 1 ). IPCC [2001, Table 6.7] gave a(cfc 11) = 0.25 W m 2 ppb 1) and a (CFC 12) = 0.32 W m 2 ppb 1). These values would yield Fa(CFC 11 + CFC 12) = W m 2 over A.D , whereas H05 computed a value of 1.04 W m 2, and Fe(CFC 11 + CFC 12) = 1.37 W m 2 (i.e., Ea(CFCs) = 1.32). To approximate the effective forcing of all MPTGs and OTGs as simulated by H05, the constants (a) are therefore increased by 1.45 from their IPCC [2001] values, which are used for the adjusted forcings Mixing Ratios of MPTGs+OTGs [39] Annual global mean atmospheric mixing ratios of the MPTGs CFC 11 and CFC 12 for A.D are taken from J. Hansen and M. Sato (Mixing Ratios of 14 Gases Controlled by the Montreal Protocol: Mixing Ratios of 12 Gases Not Controlled by the Montreal Protocol, accessed 2 June 2010, TG_A txt), and values for previous years are taken from J. Hansen and M. Sato (Global Mean Greenhouse Gas Mixing Ratios Used in GISS 2004 GCM, accessed 2 June 2010, GHGs txt) (CFC 11 and CFC 12 mixing ratios are zero prior to A.D and A.D. 1938, respectively). Mixing ratios of the other 12 MPTGs (i.e., CFC 113, CFC 114, CFC 115, CCl 4, CH 3 CCl 3, HCFC 22, HCFC 141b, HCFC 142b, HCFC 123, H 1211, H 1301, and CH 3 Br) and the 12 OTGs (i.e., HFC 134a, SF 6,CF 4,C 2 F 6, HFC 23, HFC 32, HFC 125, HFC 143a, HFC 152a, HFC 227ea, HFC 245ca, and HFC 43 10mee) for A.D are taken from Hansen and Sato (online data set, 2010). Values for previous years are taken from J. Hansen and M. Sato (Mixing Ratios of 14 Gases Controlled by the Montreal Protocol: Mixing Ratios of 12 Gases Not Controlled by the Montreal Protocol, accessed 2 June 2010, gov/modelforce/ghgases/tg_a txt) and linearly interpolated where necessary. All mixing ratios are extended to A.D by linear extrapolation from the last known annual growth rate. The resulting mixing ratios of the MPTGs and OTGs for A.D are shown in Figure 4d. [40] CF 4 is the only gas in these two groups to have a radiatively significant presence in the global atmosphere prior to A.D. 1930, suggesting that it has a preindustrial, nonanthropogenic source. Its preindustrial mixing ratio was estimated by Worton et al. [2007] to have been 34 ppt. It is assumed here to have been this value over A.D , with annual values for A.D estimated assuming a linear increase to the measured value of 40 ppt in A.D [41] Summing Fe of all MPTGs and OTGs over A.D yields 0.50 W m 2 (0.48 W m 2 over A.D ) (Table 1 and Figure 5d). These values are significantly greater than those reported by IPCC [2001] (Figure 5d) because of the high efficacy of these gases in causing surface 8of15

9 temperature change (due in part to their lack of significant absorption band overlap with the primary GHGs, although this effect may be overestimated in H05) All Well Mixed Trace Gases [42] Summing the effective radiative forcings of all wellmixed trace gases gives a net effective forcing of 3.24 W m 2 over A.D H05 computed an equivalent value of 2.61 W m 2 over A.D , and the value computed here for the same period through summing the effective forcings is almost identical (i.e., 2.63 W m 2 ), indicating consistency between the various regression fits used here and the original GCM simulations. These values are 18.5% greater than those reported by IPCC [2001] due to the efficacies of the different agents being substantially greater than 100%. [43] The series of annual well mixed gas mixing ratios assembled here for A.D , and the calibrated equations for Fe, allow Earth s radiative forcing over the past two millennia to be related to the changing mixing ratios of the well mixed anthropogenic GHGs Ozone [44] Ozone (O 3 ) is a climate forcing in both the troposphere and stratosphere. Long term increases have occurred in the troposphere due mainly to anthropogenic activities, particularly increases in emissions of CH 4,NO x, CO, and VOCs (H07). In contrast, reductions have occurred in the stratosphere due to emissions of MPTGs. Overall global mean forcing is dominated by tropospheric changes, with perhaps half of the response due to the oxidation of CH 4. H05 used estimated trends in tropospheric O 3 from a chemical transport model [Shindell et al., 2003] within a GCM, together with the stratospheric O 3 change from observations [Randel and Wu, 1999], to compute the effective direct radiative forcings due to changes in O 3 for A.D They calculated a total O 3 forcing of 0.23 W m 2 over A.D The global mean values computed by H07 (Sato and Hansen, online data set, 2010) are used here directly, with values for A.D and A.D (the Shindell et al. [2003] estimates stop at 1990) estimated from their correlation with fossil plus land use related CO 2 emissions. [45] Land use related CO 2 emissions are based on the data set of Houghton [2008], which covers A.D Values for A.D are estimated from the relationship with global human population as for fossil CO 2 emissions (see above). Land use related CO 2 emissions increase linearly with population over A.D , after which emissions increase little while population increases exponentially. A best fit of l CO2 =0.466P is obtained over A.D , where l CO2 is the land use related flux (Pg C yr 1 ) (Figure 3d). This expression is used to estimate pre A.D emissions, and values for A.D are assumed equal to the A.D rate of 1.47 Pg C yr 1. [46] An extremely tight linear relationship exists between O 3 forcing and total C emissions over A.D (Fe(O 3 ) does not increase after 1979), with a best fit of Fe(O 3 )= (f CO2 + l CO2 ) (Figure 3e). This relationship is used to estimate O 3 forcings over A.D and A.D , yielding Fe(O 3 )=0.39Wm 2 over A.D (0.31 W m 2 over A.D ) (Table 1). It is assumed that Fa(O 3 )=Fe(O 3 )/0.82 (H05) Stratospheric Water Vapor [47] Oxidation of CH 4 results in increased stratospheric H 2 O, producing a radiative forcing as an indirect consequence of CH 4 emissions. The effective radiative forcing due to stratospheric H 2 O given by H07 (Sato and Hansen, online data set, 2010) for A.D is extended to the entire A.D period using a linear regression on tropospheric CH 4 mixing ratio. As the H 2 O production rate used in the GCM calculations was based on a linear scaling with CH 4 abundance, the relationship is perfect (i.e., R 2 = 1.00), with coefficients Fe(SW) = M. Fe(SW) for A.D is then W m 2, and for the A.D period is W m 2, equal to the plausible estimate of H05 (Table 1). Efficacy of stratospheric water vapour derived from oxidation of CH 4 (i.e., Fe(SW)/Fa(SW)) is assumed to be 0.96 (= Es(SW), see below) (H05) Solar Irradiance [48] Variability in solar irradiance over the past two millennia is poorly constrained. H07 used the solar forcing of Lean [2000] (based on sunspot areas and heliocentric locations), which includes both changes in the solar constant and solar spectral changes (which are particularly large at ultraviolet wavelengths) to compute the effective forcing due to solar variability (Fe(Solar)) for A.D These data include a trend in the long term solar output, but the reality of this is highly uncertain [Lean, 2010]. [49] The more recent total solar irradiance (TSI) data set of Steinhilber et al. [2009] (data set accessed 21 May 2010 at ftp://ftp.agu.org/apend/gl/2009gl040142/2009gl ds01.txt) is 1/3rd as variable as that used by H07, with a maximum amplitude of 1.77 W m 2 ( 0.13%). This data set is used here to estimate annual TSI for A.D The reconstruction spans much of the Holocene (i.e., A.D ) and is based on the abundance of cosmogenic radionuclide 10 Be in polar ice. There is debate concerning the level of relevant information in this proxy [Lean, 2010], but it is currently the only fully consistent estimate over this time scale. The original data are 40 year running means resampled to 5 year intervals, and annual values for A.D are derived here by linear interpolation. Anomalies are then applied to a recent value of the A.D solar minimum estimated from Figure 3 of Kopp et al. [2005] to be W m 2, rather than that reported by Steinhilber et al. [2009] (i.e., W m 2 ). Annual mean TSI values for A.D and A.D are estimated from Figure 1 of Lean [2010], yielding W m 2 and W m 2, respectively. The change in these TSI values over time is then used as direct input to the EBM. Fe(Solar)/Fa(Solar) is assumed to equal 0.92 (H05) Land Use [50] H05 computed the effective radiative forcing due to land use changes for A.D , as specified in the data set of Ramankutty and Foley [1999], to be 0.09 W m 2. The major effect is due to increases in albedo following removal of natural vegetation for croplands in northern midlatitudes. The annual global mean land use radiative forcing for A.D reported by Sato and Hansen (online data set, 2010) and H07 is used here directly. It is also extended back to 1 A.D. and forward to A.D using the relationship 9of15

10 between the computed forcing and the estimated land use related CO 2 emissions, l CO2 (see above). This relationship is derived over A.D by hand fitting the intercept to ensure continuity with values before A.D. 1880, giving Fe(LU) = l CO2 (Figure 3f). Effective forcing due to land use changes over A.D is then estimated to have been 0.17 W m 2 ( 0.14 W m 2 over A.D ) (Table 1). Efficacy of land use radiative forcing is assumed to be 1.02 (H05) Snow Albedo [51] Reductions in snow and ice albedos due to deposition of black carbon (BC), while highly uncertain, are believed to be a significant climate forcing [Hansen and Nazarenko, 2004]. H07 computed the effective forcing due to these changes in snow albedo for A.D using albedo changes specified in the GCM in proportion to the time varying local BC deposition calculated off line by Koch [2001]. Fe(SNW) was computed to be 0.15 W m 2 over A.D , with the forcing held constant over A.D (Sato and Hansen, online data set, 2010). These estimates are extended here to the A.D period using relationships with fossil CO 2 emissions calculated as described above. [52] Computed Fe(SNW) increases rapidly with emissions to A.D. 1890, with a best fit regression over A.D of Fe(SNW) = f CO2 (Figure 3g). This relation is used to extrapolate Fe(SNW) over A.D Values for A.D are derived by extrapolating the computed relationship with fossil CO 2 emissions in the latter part of the time series (Figure 3h). The relation Fe(SNW) = f CO2 was obtained over A.D (Figure 3h). Effective forcing due to BC effects on snow and ice albedos is then estimate to have been 0.23 W m 2 over A.D (0.18 W m 2 over A.D ) (Table 1). Efficacy of BC affected albedo radiative forcing is assumed to be 2.7 (H07) Stratospheric Aerosols [53] Volcanic eruptions can cause large transitory perturbations to global tropospheric temperatures through injection of aerosols into the stratosphere. Their effective annual global mean radiative forcing for A.D is calculated here by summing the forcings of Hegerl et al. [2006] over their four latitudinal regions. These estimates are derived from a composite sulphate flux derived from nine ice cores. Values for A.D are estimated from the ice core derived data set of Ren et al. [2010]. [54] A simple model of injection and decay is fitted to the effective forcing computed by H05 resulting from the Agung eruption in A.D DFeðSA Þ ¼ ðsulðþþsul t ðt 1ÞÞ FeðSAÞ; ð16þ where sul ( f/f T = relative to Tambora in 1815) is the sulphate record of Ren et al. [2010], t is time (years), a = 5.31 Wm 2 ( f/f T ) 1, and b = [55] The resulting time series of volcanic forcing displays fewer events prior to A.D than after, when there are far more smaller events. This is presumably at least partly because of the lower sensitivity of the methodology employed by Ren et al. [2010]. Efficacy of radiative forcing due to stratospheric aerosols is assumed to be 0.91 (H05) Black Carbon [56] The direct effective forcing by BC tropospheric aerosols for A.D is estimated as for snow albedo. Fe(BC) increases rapidly with emissions to A.D. 1900, with a best fit regression over A.D of Fe(BC) = f CO2 (Figure 3g). This relation is used to extrapolate Fe(BC) over A.D Values for A.D are derived by extrapolating the computed relationship with fossil CO 2 emissions in the latter part of the time series. The relation Fe(BC) = f CO2 is obtained over A.D (Figure 3h). [57] Effective forcing due to direct tropospheric BC effects is then estimated to have been 0.69 W m 2 over A.D (0.54 W m 2 over ) (Table 1). BC efficacy is assumed to be 0.68 (H05) Reflective Aerosols [58] The radiative forcing by reflective aerosols is highly uncertain. Values for their direct effective forcing are calculated here for A.D based on the simulation results of H07, with a methodology as used for the direct effects of BC. A best fit regression over A.D of Fe(RA) = f CO2 is obtained (Figure 3g). This relation is used to extrapolate Fe(RA) over A.D Values for A.D are derived by extrapolating the computed relationship with fossil CO 2 emissions in the latter part of the time series. The relation Fe(RA) = f CO2 is obtained over A.D (Figure 3h). [59] Effective forcing due to reflective aerosols over A.D is then estimated to have been 1.43 W m 2 ( 1.20 W m 2 over A.D ) (Table 1). Efficacy of reflective aerosols is assumed to be 1.08 (H05) Aerosol Indirect Effect [60] The effective radiative forcing due the aerosol indirect effect (AIE) computed by H05 is extended over A.D as for reflective aerosols by exploiting the tight linear relationships with anthropogenic CO 2 emissions. A best fit regression over A.D of Fe(AIE) = f CO2 is obtained (Figure 3g). This relation is used to extrapolate Fe(AIE) over A.D Values for A.D are derived by extrapolating the computed relationship with fossil CO 2 emissions in the latter part of the time series. The relation Fe(AIE) = f CO2 is obtained over A.D (Figure 3h). [61] Effective forcing due to the AIE over A.D is then estimated to have been 0.97 W m 2 ( 0.87 W m 2 over A.D ) (Table 1). H05 did not calculate the value of Ea for the AIE. However, they did report Es(AIE) (i.e., the efficacy using fixed SST, but allowing the stratosphere, troposphere, and land surface temperatures to adjust) for the cloud cover effect equal to 0.97 ± 0.08, and so Ea(AIE) is taken to be Net Forcing [62] The magnitude of positive and negative forcings by the ten agents considered here are shown in Figure 6. Notable features are the highly variable contributions of CO 2, solar, and volcanic activity over A.D (Figure 6a), the coincidence of reduced CO 2 forcing, reduced solar forcing, and increased volcanic forcing during the 17th century (Figure 6a), and the accelerating increase in anthropogenic 10 of 15

11 Figure 6. Estimated global mean effective radiative forcings. (a) Major forcings, A.D (other forcings are not visible on this scale). (b) All forcings, A.D forcings from the late 18th century, totally obscuring all natural forcings from the early 19th century apart from volcanic aerosols (Figure 6b). [63] Summed effective radiative forcing over A.D is 2.00 W m 2 (Table 1) (1.83 W m 2 over A.D ) (Table 1). H05 estimated a summed value of 1.82 W m 2 for A.D (calculated from their Figure 28). However, the similarity of this net figure with that in Table 1 hides some significant differences between individual forcings. In particular, Fe(Solar) is lower here than in H05 by 0.27 W m 2, whereas forcings due to CO 2, MPTGs+OTGs, O 3, reflective aerosols, and the AIE are all significantly higher. [64] H05 computed the effective forcing of all agents acting at once over A.D to be 1.69 W m 2. The difference with their arithmetic sum of individual forcings, 1.85 W m 2, is mainly due to spatial overlaps between different forcings. A correction to the combined (summed) effective forcings estimated here for input to the EBM is therefore necessary, and is taken as 0.91, yielding Fe(Net). The resulting time series of total net effective forcing over A.D is shown in Figure 7. Also shown in Figure 7 is the net adjusted forcing using the same correction factor for interactions between forcings. Fe is lower than Fa primarily because of the low efficacy of tropospheric BC. 4. Uncertainty Analysis [65] Prediction uncertainty in annual temperature over A.D was assessed with respect to all model inputs, including parameter values. It was assumed that each input can be varied independently and that each value within the stated range is equally likely (i.e., uniform distribution). Uncertainty with respect to alternative volcanic and solar forcing data sets was also assessed (see below). [66] Where possible, the ranges of each model input were chosen on the basis of estimates from literature values, otherwise best guesses were made. Ranges are given in Table 2. [67] A range of possible values for the net feedback factor was calculated from the range of GCM sensitivities to doubled atmospheric CO 2 given in Table 8.2 of Randall et al. [2007], assuming no feedback warming of K. [68] The default correction to the total net forcing derived from the GISS GCM simulation results is Without further knowledge, the possible range was simply specified as 10% around this value. [69] The e folding time of the fast thermal component was varied over 1 3 years. This then specifies the time constants of all components. The associated relative contributions from the fast and medium components were varied over the ranges and , respectively. This combination of ranges specifies a wide range of thermal properties. [70] Forcings were varied using a constant scalar applied to the anomalies across all years in each simulation. The scalar ranges for CO 2,CH 4, CFCs, ozone, land use, reflective aerosols, and the aerosol indirect effect were derived from the range of uncertainties discussed in previous sections and by H05. The scalar for solar forcing was specified as to include the 3 greater forcing of the Lean [2000] data set than the default used here. Uncertainties in forcings due to snow albedo, black carbon, and stratospheric aerosols were harder to ascertain, and so their scalars were simply set to to cover a relatively wide range of possible values. [71] Importance of model inputs for each annual prediction was computed as the ratio of the variance of the conditional expectation (VCE) to total prediction variance, the correlation ratio of Kendall and Stuart [1979] (h 2 ;computed as detailed by McKay [1995]). Sampling of each input across its estimated range was made using a random number generator. Accurate estimates of h 2 could be obtained with a sample size of 50,000 for the conditional annual expected values and 1,000 replicates of each input, giving 50,000,000 model runs for each annual estimate of h 2. The results are given in Table 2 as means of h 2 over the pre industrial and industrial periods. In addition, the mean and 95% limits of the annual prediction probability distributions obtained when all inputs are varied are shown in Figures 8 and 9. [72] Prediction uncertainty with respect to volcanic and solar forcing data sets was assessed using default parameters and forcings. The data sets used are given in Table 3, and all Figure 7. Net forcings of all 10 agents, A.D of 15