Figure 6. Contribution of external forcing to reconstructed decadal mean temperature. The top panel shows CH-blend and the instrumental record compared to simulations with an Atmosphere-Ocean General Circulation model and an EBM forced with estimates of volcanic, solar, and anthropogenic forcing (EBM simulation with natural forcing only dashed). The simulations are scaled to best fit the reconstruction (90% confidence interval for EBM fingerprint shaded). The bottom panel shows an estimate of the contribution to CH-blend (long) from individual forcings (volcanism, solar forcing, and greenhouse gas and aerosol forcing combined) and the associated 90% uncertainty range for the detectable signals, which are marked by an asterisk (*). Forcing fingerprints are centered to the period analyzed. Figure 7. Similar as Figure 6, but comparing detection results to those for other high variance reconstructions. The top panel compares reconstructions by Esper et al. 2002, Moberg et al., 2005, Briffa et al., 2001 and CH-blend (details see table 2) with NH 30-90N average temperature from an EBM simulation forced with volcanic, solar, and anthropogenic forcing combined and instrumental data (green line). All top panel data are smoothed removing variance below 20 yrs, bottom panel data show fingerprints in the decadal time domain used for detection. The bottom panel compares the contribution from individual forcings (volcanism, solar forcing, and greenhouse gas and aerosol forcing combined, scaling factor see table 2) to individual records: Briffa (solid, fat), Esper (dotted), Moberg (dashed) and Ch-blend (solid, thin, shown with associated 90% uncertainty range). Forcing fingerprints are centered to the period analyzed. Figure A1: Decadally smoothed or decadal proxy sites used for the reconstructions in standard deviation units. The records are explained in Appendix A. LETTERS Climate sensitivity constrained by temperature reconstructions over the past seven centuries Gabriele C. Hegerl', Thomas J. Crowley', William T. Hyde1 & David J. Frame2 The magnitude and impact of future global warming depends on the sensitivity of the climate system to changes in greenhouse gas concentrations. The commonly accepted range for the equilibrium global mean temperature change in response to a doubling of the atmospheric carbon dioxide concentration', termed climate sensitivity, is 1.5-4.5 K (ref. 2). A number of observational studies, however, find a substantial probability of significantly higher sensitivities, yielding upper limits on climate sensitivity of 7.7K to above 9K (refs 3-8). Here we demonstrate that such observational estimates of climate sensitivity can be tightened if reconstructions of Northern Hemisphere temperature over the past several centuries are considered. We use large-ensemble energy balance modelling and simulate the temperature response to past solar, volcanic and greenhouse gas forcing to determine which climate sensitivities yield simulations that are in agreement with proxy reconstructions. After accounting for the uncertainty in reconstructions and estimates of past external forcing, we find an independent estimate of climate sensitivity that is very similar to those from instrumental data. If the latter are combined with the result from all proxy reconstructions, then the 5-95 per cent range shrinks to 1.5-6.2 K, thus substantially reducing the probability of very high climate sensitivity. We use four palacoreconstructions, namely a hemispheric reconstruction of mean annual temperatures", a maximum latewood density tree ring based reconstruction" for growing season temperatures over 20-90° N land, a revised and smoothed version of a record" that has been calibrated to 30-90°N land annual data", and our own new decadal reconstruction termed 'CH-blend' of annual average 30-90° N temperature's (Fig. 1). A version of CH-blend using 12 records extends from AD 1505 to AD 1960; and a reconstruction based on 9 sites ('CH-blend (long)') is used from AD 1270. Both reconstructions use a relatively small number of well spaced sites (often based on multiple records, including some regional reconstructions) throughout the reconstruction. CH-blend is consistent with independent estimates of temperatures from boreholes', and both CH-blend and CH-blend (long) agree well with a recent reconstruction" that incorporates records of lower temporal resolution. The reconstruction method has been tested using noise-perturbed climate model data from the same locations as used in the reconstruction". Results show that the reconstruction of decadal temperatures is accurate and reliably preserves the variance of hemispheric-scale temperature variability. techniques underestimate past climate variability" (for details see Supplementary Information). We conduct a large ensemble (>1,000) of simulations of the past 1,000 years with a 2.5-dimensional (latitude/longitude/depth) upwelling-diffusion energy balance model (EBM), with realistic land-sea distribution. The EBM is a variant of a seasonal model" that simulates time-dependent responses to external forcing, and includes the seasonal cycle (for details see Supplementary Information). The same model has been previously used to examine the relationship between reconstructed temperature and external forcing over the past millennium1.20. EBM simulations reproduce the largescale temperature response of general circulation models, and have the advantage of being able to generate large ensembles. The following two model parameters are important determinants of the large-scale response of climate models to external forcing and have been systematically varied in our ensemble. First, the equilibrium climate sensitivity to a doubling of CO2, a, which was varied in 0.5 K increments from 0.5 K to 10.0 K with an additional low value of 0.25 K. Second, effective ocean diffusivity x in the upwelling-diffusive model, which was varied between 0.63 cm2s and 3.8 cm's'. 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 Figure 1 Palaeoclimatic records compared to a climate model simulation. For CH-blend, our estimate of climate sensitivity fully accounts for the uncertainty in the amplitude of the record". For the other reconstructions, we use both the published reconstruction and a version that is recalibrated using our technique. This approach avoids introducing a low bias in our estimate of climate sensitivity based on the possibility that some reconstruction 'Division of Earth and Ocean Sciences, Nicholas School of the Environment and Earth Sciences, Duke University, Durham, North Carolina, 27708, USA. Climate Dynamics Group, Department of Physics, University of Oxford, Oxford OX1 3PU, UK. 1029 Probability density function Figure 2 | Northern Hemisphere mean radiative forcing. Sub-annual forcing data are used in the climate model simulations, but a decadal filter is applied here for illustration only, to focus on timescales most relevant for the analysis. For tropospheric aerosol forcing (green), a range of forcing has been used; for solar (pink) and volcanic (blue) forcing, a best guess forcing (dark, thick line) and a gaussian uncertainty range has been used (2.5% and 97.5% limits are shown by light, thin lines, the lower limit for solar is on the zero line). For clarity, greenhouse gas (GHG') and aerosol forcings are offset by 3 Wm2, and solar forcing by I Wm2. This range embraces an observational estimate of 1.7 ± 0.2 cm2 s based on a global compilation of GEOSECS data of bomb tritium penetration into the world ocean" and a lower range based on bomb C of the order of 1 cm2 s1. We have further tested our range of diffusivities by comparing simulated ocean warming with ocean heat content data. We find that the smaller to mid-range values of x yield results that compare most favourably with these data, consistent with the observation that most of the twentieth-century increase in ocean heat content is in the upper 1,000 m (Supplementary Fig. 1). Note that ocean diffusivity is of smaller importance for the simulations of the pre-industrial period, where forcings are mostly episodic and relatively small, than for the twentieth century. In the latter period, the rate of temperature increase is crucially influenced by ocean diffusivity, as large diffusivities tend to hide more warming in the oceans than small diffusivities (see Supplementary Information for more discussion). Our results are insensitive to attempts to constrain further. They are, however, conditional on ocean effective diffusivity being within the range we use. Prior work',19,20,25 has established that various reconstructions of hemispheric temperature consistently show influence from volcanism and greenhouse gas variations, and less consistently from variations in solar radiation. We force the EBM simulations with a combination of solar, volcanic, greenhouse gas and tropospheric aerosol forcing to simulate hemispheric temperature change over the past millennium (Fig. 2). Greenhouse gas forcing is based on changes in trace gases from ice-core data, combined with IPCC estimates of radiative forcing for well-mixed greenhouse gases in the twentieth century. The estimate of solar forcing is based on "C data, scaled to the solar irradiance reconstruction of ref. 27 after reducing its amplitude by 20% to accommodate recent conclusions that the former estimate may have been large. For volcanism, we use an update of a global reconstruction based on ice-core data from Greenland and Antarctica. We account for the considerable uncertainty in solar and volcanic forcing by varying the total amplitude of each forcing time-series around its central estimate. We use Monte Carlo simulations based on a 50% standard deviation for solar forcing, and a 35% standard deviation for volcanic forcing (excluding the unphysical case of net negative forcing). The uncertainty in our results due to random errors in the magnitude of individual volcanic eruptions was estimated by sensitivity tests, indicating that errors in the magnitude of individual eruptions can cause a modest widening of the tail of the distribution (Supplementary Fig. 2; see Supplementary Information for more detail on forcings and their uncertainty). We derive a probability density function (PDF) for climate sensitivity using a method related to one previously used for instrumental data (see Methods section, and algorithm in Supplementary Information). Results for the CH-blend reconstruction, for which we have the most reliable uncertainty estimate', yield a 5-95% range for sensitivity of 1.4 K to 6.1 K and a median sensitivity of 2.6 K over the pre-instrumental period 1505–1850 (Fig. 3a). PDFs for climate sensitivity from the other reconstructions and the same period yield peak probabilities (modes) from 1.3K to 3.6 K, and some of them suggest a moderate probability for climate sensitivity being high (see Supplementary Table 4). Reconstructions with higher amplitudes of past climate fluctuations generally suggest higher climate sensitivities than those with low variability. The range of the other free parameters, ocean diffusivity x, and solar and volcanic forcing uncertainty, are used to fully explore uncertainties rather than to provide posterior information about best-fit values. Figure 3 | Estimated probability density functions (PDFs) for equilibrium climate sensitivity to CO2 doubling (in K). a, PDFs from a range of palaeoreconstructions using data to 1850 (dotted lines, based on rescaled data). The horizontal bars indicate the 5-95% range of PDFs (median is indicated by a dot, and 10th and 90th percentiles by a vertical bar). 1030 b, Comparison to other estimates of climate sensitivity based on instrumental data4.67 over the twentieth century or 1950-2000". All PDFs have been scaled to integrate to 1 between 0 and 10 for better comparison. < Combined estimate using a result from instrumental data" as prior distribution, updated by the result from pre-industrial data ('w.p.'). |